Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961On Hilbert geometryENYasuoNasuNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961On general connections IIENTominosukeOtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961Über die Koeffizienten der schlichten Funktionen (II)ENKen'itiKosekiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961Über die p-wertigen FunktionenENKen'itiKosekiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661021961On Galois and locally Galois extensions of simple ringsENTakashiNagaharaHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On conformal collineationsENYoshihiroTashiroNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On generating elements of Galois extensions of division rings VENTakasiNagaharaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960Spectral theory of operator algebras IIENMinoruTomitaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On some properties of group characters IIENMasaruOsimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960Beiträge zur Theorie der schlichten FunktionenENKen'itiKosekiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15661011960On Galois theory of division rings IIIENNobuoNobusawaHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Self Maps of Suspension of Sphere Bundles over SpheresENHideoTakahashiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Anti-Intergral Elements and Coefficients of their Minimal PolynomialsENSusumuOdaKen-ichiYoshidaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Theta Functions, IIENTakashiTasakaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Hopf Maps and TrialityENA.RigasLucas M.ChavesNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Multiplicative Elements in Morava K-Theory of BZ/pENK.KordzayaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996On the Differential Submodules of ModulesENMamoruFuruyaHiroshiNiitsumaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996On Values of Cyclotomic Polynomials. IIIENKaoruMotoseNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Orthogonality in the Category of ComplexesENEdger E.EnochsOvertoun M. G.JendaJinzhongXuNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Weakly Henselian RingsENThomasMckenzieNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Note on Homotopy Classes of Self Maps; [ΣHP³, ΣHP³]ENHideoTakahashiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996The Property Special (DF) for Unit-Regular RingsENMamoruKutamiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Panes, Nets, and CodesENSteven T.DoughertyNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996A Remark on Torsion-Free Subgroups in Group RingsENTôruFurukawaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663811996Infinite Galois Theory of Semisimple RingsENKazuyukiTanabeNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Elliptic Curves y²=x³-px of Rank TwoENBlair K.Spearman<p>A class of prime numbers p is given for which the elliptic curve y² =x³-px has rank two. This extends a theorem of Kudo and Motose.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Evaluation of the Convolution Sums ∑ l+24m=n σ(l) σ(m) and ∑ 3l+8m=n σ(l) σ(m)ENAyseAlacaSabanAlacaKenneth S.WilliamsNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Galois Covers of Degree p and Semi-stable Reduction of Curves in Equal Characteristic p>0ENMohamedSaïdi<p>In this paper we study the semi-stable reduction of Galois covers of degree p above curves over a complete discrete valuation ring of equal characteristic p.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007A Characterization of δ-quasi-Baer RingsENEbrahimHashemi<p>Let δ be a derivation on R. A ring R is called δ-quasi-Baer (resp. quasi-Baer) if the right annihilator of every δ-ideal (resp. ideal) of R is generated by an idempotent of R. In this note first we give a positive answer to the question posed in Han et al. [7], then we show that R is δ-quasi-Baer iff the differential polynomial ring S = R[x; δ] is quasi-Baer iff S is δ‾-quasi-Baer for every extended derivation δ‾ on S of δ. This results is a generalization of Han et al. [7], to the case where R
is not assumed to be δ-semiprime.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007A Generalized Primitive Element TheoremENDirceuBagioAntonioPaques<p>We deal with the following variant of the primitive element theorem: any commutative strongly separable extension of a commutative ring can be embedded in another one having primitive element. This statement holds for connected strongly separable extension of commutative rings which are either local or connected semilocal. We show that it holds for a more general family of rings, that is, for connected commutative rings whose quotient ring by the corresponding Jacobson radical is von Neumann regular and locally uniform. Some properties of the (connected) separable closure of such rings are also given as an application of this result.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Sums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional CalculusSums and Partial Sums of Double Power Series associated with the Generalized Zeta Function and Their N-fractional CalculusENMaged G.Bin-Saad<p>An attempt is made here to introduce and study a pair of
double power series associated with the generalized zeta function due to Erdélyi Φ(x; z; a) together with related sums, integral representations,
generating relations and N-fractional calculus. A number of (known and
new) results shown to follow as special cases of our theorems.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Higher Weights of Codes from Projective Planes and BiplanesENSteven T.DoughertyReshmaRamadurai<p>We study the higher weights of codes formed from planes
and biplanes. We relate the higher weights of the Hull and the code of a plane and biplane. We determine all higher weight enumerators of planes and biplanes of order less or equal to 4.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007On Ideals and Orthogonal Generalized Derivations of Semiprime RingsENEmineAlbas<p>In this paper, some results concerning orthogonal generalized derivations are generalized for a nonzero ideal of a semiprime ring. These results are a generalization of results of M. Brešar and J. Vukman
in [3], which are related to a theorem of E. Posner for the product of derivations on a prime ring.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Some Results on (σ,τ)-Lie IdealsENEvrimGüvenKazimKayaMuharremSoytürk<p>In this note we give some basic results on one sided(σ,τ)-Lie ideals of prime rings with characteristic not 2.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Some Questions on the Ideal Class Group of Imaginary Abelian FieldsENTsuyoshiItoh<p>Let k be an imaginary quadratic field. Assume that the
class number of k is exactly an odd prime number p, and p splits into two distinct primes in k. Then it is known that a prime ideal lying above p is not principal. In the present paper, we shall consider a question whether a similar result holds when the class number of k is 2p. We
also consider an analogous question for the case that k is an imaginary quartic abelian field.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Character Values and Dade's ConjectureENRyoNarasakiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Privalov Space on the Upper Half PlaneENYasuoIida<p>In this paper, we shall consider Privalov space Np 0 (D) (p > 1) which consists of holomorphic functions f on the upper half plane D := {z ∈ C|Imz > 0} such that (log+ |f(z)|)p has a harmonic majorant on D. We shall give some properties of Np 0 (D).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Generalized Derivations with Commutativity and Anti-commutativity ConditionsENHoward E.BellNadeem-urRehman<p>Let R be a prime ring with 1, with char(R) ≠ 2; and let F : R → R be a generalized derivation. We determine when one of the following holds for all x,y ∈ R: (i) [F(x); F(y)] = 0; (ii) F(x)ΟF(y) = 0;
(iii) F(x) Ο F(y) = x Ο y .</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007Cut Loci and Distance FunctionsENJin-ichiItohTakashiSakaiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002A Representation of Ring Homomorphisms on Unital Regular Commutative Banach AlgebrasENTakeshiMiura<p>We give a complete representation of a ring homomorphism from a unital semisimple regular commutative Banach algebra into a unital semisimple commutative Banach algebra, which need not be regular. As a corollary we give a sufficient condition in order that a ring homomorphism is automatically linear or conjugate linear.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002On the Nilpotency Index of the Radical of a Group Algebra. XIENKaoruMotoseNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Hopf Algebra Structure of Morava K-Theory of the Exceptional Lie Groups, IIENTetsuNishimotoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Note on the Relation between S-reducibility, S-coreducibility and Stable Homotopy Types of Some Stunted Lens SpacesENYasusukeKotaniNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Ladder Index of GroupsENKazuhiroIshikawaHiroshiTanakaKatsumiTanakaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002On Commutativity of Rings with Generalized DerivationsENNadeem urRehman<p>The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for all x, y ∈ R, where d is a derivation on R, such a function F is said to be a generalized derivation. In the present paper we have discussed the commutativity of prime rings admitting a generalized derivation F satisfying (i) [F(x), x] = 0, (ii) F([x, y]) = [x, y], and (iii) F(x ◦ y) = x ◦ y for all x, y in some appropriate subset of R.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002On the Group π(ΣA×B,X)ENSeiyaSasaoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Decomposition of Spinor Groups by the Involution σ' in Exceptional Lie GroupsENToshikazuMiyashitaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Semigroups of Locally Lipschitz OperatorsENYoshikazuKobayashiNaokiTanakaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664412002Geometry on Grassmann Manifolds G(2,8) and G(3,8)ENZhouJianweiHuangHui<p>In this paper, we use the Clifford algebra Cℓ<sub>8</sub> to construct fibre bundles ¿<sub>1</sub> : G(2; 8) → S<sup>6</sup>, ¿'<sub>1</sub> : G(2; 7) → S<sup>6</sup> and ¿<sub>2</sub> : G(3; 8) → S<sup>7</sup>, the fibres are CP<sup>3</sup>, CP<sup>2</sup> and ASSOC = G<sub>2</sub>=SO(4) respectively. We show that G(2; 5), CP<sup>3</sup> and S<sup>6</sup> are the homologically volume minimizing submanifolds of G(2; 8) by calibrations and they generate the homology group H<sub>6</sub>(G(2; 8)). The submanifolds S<sup>7</sup> and ASSOC of G(3; 8) generate H<sub>7</sub>(G(3; 8)) and H<sub>8</sub>(G(3; 8)) respectively.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008Inverse Limits of Spaces with the Weak B-PropertyENZhaoBinNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008The Fine Spectra of the Cesàro Operator C 1 over the Sequence Space bvp, (1 ≤ p ∞)ENAli M.AkhmedovFeyziBasar<p>The sequence space bvp consisting of all sequences (xk) such that (xk - xk-1) in the sequence space lp has recently been introduced by Basar and Altay [Ukrainian Math. J. 55(1)(2003), 136-147]; where 1 ≤ p ≤ ∞. In the present paper, the norm of the Cesàro operator C1 acting on the sequence space bvp has been found and the fine spectrum of the Cesàro operator C1 over the sequence space bvp has been determined, where 1 ≤ p < ∞.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008A Lower Bound for the Rational LS-category of a Coformal Elliptic SpaceENToshihiroYamaguchi<p>We give a lower bound for the rational LS-category of certain spaces, including the coformal elliptic ones, in terms of the dimension of its total rational cohomology.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Central Gap Numbers of Symmetric GroupsENHirotakakikyo<p>g(G) denotes the central gap number of a group G. We
show that for n ≥ 8, g(Sn) ≥ n and g(An) ≥ n-2. We give exact values of g(Sn) and g(An) for small n's. In particular, g(S9) = 9 and g(A9) = 7. Therefore, for any positive integer n ≠ 1, 3, 5 there is a group G such that n = g(G). G can be finite or infinite.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Fox Spaces and Jacobi IdentitiesENMarekGolasinskiDaciberg LimaGonçalvesPeterWong<p>In 1945, R. Fox introduced the so-called Fox torus homo-
topy groups in which the usual homotopy groups are embedded and their Whitehead products are expressed as commutators. A modern treatment of Fox torus homotopy groups and their generalization has been given and studied. In this note, we further explore these groups
and their properties. We discuss co-multiplications on Fox spaces and Jacobi identities for the generalized Whitehead products and the T- Whitehead products.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008Imaginary Quadratic Fields whose Exponents are Less Than or Equal To TwoENKenichiShimizu<p>We give a necessary condition for an imaginary quadratic
field to have exponent less than or equal to two. Further we discuss relations of this condition with other necessary conditions studied by Möller and Mollin, and conjecture that these conditions are equivalent.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Φ-recurrent N(k)-contact Metric ManifoldsENUday ChandDeAboul KalamGazi<p>In this paper we prove that a Φ-recurrent N(k)-contact metric manifold is an η-Einstein manifold with constant coefficients. Next, we prove that a 3-dimensional Φ-recurrent N(k)-contact metric manifold
is of constant curvature. The existence of a Φ-recurrent N(k)-contact metric manifold is also proved.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008A New Class of Quasicyclic Complex Vector Functional EquationsENIce B.Risteski<p>For the first time in the literature a quasicyclic complex vector functional equation is introduced in the present paper. By a matrix method the general quasicyclic complex vector functional equation is solved, as well as its particular case for n = 3. This case is completely solved in an explicit form, and for every step of the solution examples are provided. Using a simple spectral property of compound matrices, a necessary and sufficient condition for stability of the quasicyclic complex vector functional equation considered is proved.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008K-semimetrizabilities and C-stratifiabilities of SpacesENIwaoYoshiokaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008On Unit Groups of Completely Primary Finite RingsENChiteng'a JohnChikunji<p>Let R be a commutative completely primary finite ring with the unique maximal ideal J such that J3 = (0) and J2 ≠ (0): Then R⁄J ≅ GF(pr) and the characteristic of R is pk, where 1 ≤ k ≤ 3, for
some prime p and positive integers k, r. Let Ro = GR (pkr,pk) be a galois subring of R so that R = Ro ⊕ U ⊕ V ⊕ W, where U, V and W are finitely generated Ro-modules. Let non-negative integers s, t and be numbers of elements in the generating sets for U, V and W, respectively. In this work, we determine the structure of the subgroup 1+W of the unit group R* in general, and the structure of the unit group R* of R when s = 3, t = 1; ≥ 1 and characteristic of R is p. We then generalize the solution of the cases when s = 2, t = 1; t = s(s +1)⁄2 for a fixed s; for all the characteristics of R ; and when s = 2, t = 2, and characteristic of R is p to the case when the annihilator ann(J ) = J2 + W, so that ≥ 1. This complements the author's earlier solution of the problem in the case when the annihilator of the radical coincides with the square of the radical.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665012008Strong Convergence Theorems for Nonexpansive Mappings by Viscosity Approximation Methods in Banach SpacesENXiaolongQinYongfuSuChangqunWu<p>In this paper, we introduce a modified Ishikawa iterative process for a pair of nonexpansive mappings and obtain a strong convergence theorem in the framework of uniformly Banach spaces. Our results improve and extend the recent ones announced by Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51-60], Xu [H.K. Xu, Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl. 298 (2004) 279-291] and some others.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Some Examples of Benford SequencesENKazuoGotoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Derivations in Near-rings and RingsENHoward E.BellGordonMasonNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Curvature Forms and Einstein-like Metrics on Sasakian ManifoldsENElsaAbbenaSergioGarbieroNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Degree Equations for p-blocks of Finite Group, IIENKazuokiIkedaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Generalized Tilting Modules and Applications to Module TheoryENYoichiMiyashitaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Subrings Containing IdealsENShalomFeigelstockNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Real Hypersurfaces in Pn(C) with Constant Principal CurvaturesENU-HangKiRyoichiTakagiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Commutativity of a Certain Class of RingsENHiroakiKomatsuTsunekazuNishinakaAdilYaqubNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Uncoutably Many Infinite Loop Spaces of the Same N-type for all NENYoshimiShitandaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Some Characterizations of Right co-H-ringsENDinh VanHuynhPhanDanNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992π-regular Rings Satisfying the Converse of Schur's LemmaENChol OnKimChanHuhNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Primitive Elements for Cyclic p^n -extensions of Commutative RingsENAnnetta G.AramovaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Prime Ideals in Strongly Graded Rings by Polycyclic-by-finite Groups IIENHidetoshiMarubayashiHaruoMiyamotoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Pseudo-riemannian Submanifolds with Pointwise Planar Normal SectionsENYoung HoKimNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Finite Posets P and P-galois Extensions of RingsENKazuoKishimotoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On H-separable Polynomials in Skew Polynomial Rings of Automorphism TypeENShoichiIkehataGeorgeSzetoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Degrees of Self-mapsENAkiraSasaoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Jordan Left DerivationsENQingDengNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Global Dimension of 2x2 Generic Trace Zero Matrices and Invariants of 2x2 Generic MatricesENChanHuhNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On the (2,3)-closures of IdealsENSusumuOdaKen-IchiYoshidaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992An Example of an Indecomposable Module which is not InjectiveENShojiMorimotoTakefumiShudoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992Signatures on a RingENTeruoKanzakiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On Some Products of β-elements in the Homotopy of the Moore SpectrumENMihoMabuchiKatsumiShimomuraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992On the Nilpotency Index of the Radical of a Group Algebra. XENKaoruMotoseNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992A Note on the Lie Group G2 as a Framed BoundaryENMasaakiYokotaniNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663411992The Integral Cohomology Rings of F4/Spin(n) and E6/Spin(m)ENMasaakiYokotaniNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Notes on Basic RingsENMasaruOshimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Theorie der Derivationen und KörperdifferentenENMikaoMoriyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Contribution á la Topologie IIENTakeshiInagaki<p>On croit en général que la théorie topologique dans un espace
se développe en relation avec la propriété topologique de l'espace
considéré. Cependant, si l'on envisage les notions utilisées pour
établir la théorie, on voit sans peine qu'il y a deux espéces de notions,
c.-á-d. que les unes sont en relations intimes avec la topologie de l'espace
et les autres, presque indépendantes de la topologie de l'espace. Par
exemple, la notion d'un ensemble fermé est bien définie en relation
intime avec la topologie de l'espace considéré et la notion de l'ensemble
mesurable ß se rapporte certainement á la puissance ℵ<sub>0</sub> ,
mais il sera plus naturel de dire qu'elle est presque indépendante de
la topologie de l'espace.
Pour mettre en lumière ce que nous avons rapporté plus haut,
nous montrons un exemple. Si l'on regard l'ensemble dit homogenen
Normaltypus η<sub>ξ</sub> comme un espace dans lequel, comme toujours, les
voisinages d'un point x sont d'intervalles ouverts contenant le point
x, alors, comme on le voit sans peine, la SQ1nme de nombre dénombrable
d'ensembles fermés l'est également; par conséquent, dans cet
espace la notion de l'ensemble F<sub>σ</sub> au sens usuel n'a aucun sens essentiel,
et on voit que dans cet espace l'ensemble correspondant à
l'ensemble F<sub>σ</sub> doit être défini comme une somme de la puissance ℵ<sub>ξ</sub>
d'ensembles fermés.
Originellement, la topologie prend sa source à la notion de la.
limite et il me semble donc qu'il est naturel de développer sa théorie
en relation avec la structure de la limite dans l'espace que nous
avons en question.
Soient R un espace υ introduit par M. Fréchet et χ un point de·
R. Alors, il y a plusieurs familles de voisinages du point χ telles
qu'elles sont équivalentes deux à deux, et de plus il y a une famille
telle que sa puissance est la plus petite parmi celles de toutes les
familles. Désignons respectivement par {V(χ)} et ℵ(χ), la famille
et sa puissance. Cela posé, si un système ordonné de points {χ<sub>χ</sub>}
converge vers le point χ, alors, comme on le sait, on peut convenablement
extraire un système {χ<sub>v(χ)</sub>}, se composant de points de {χ<sub>χ</sub>}
et ordonné suivant l'ordre de l'ensemble {V(χ)} de leurs suffixes, tel
qu'il converge vers le point χ; ce qui Inontre que la convergence
vers le point x peut être écrite par le mot de la convergence d'un
système ordonné de la puissance ℵ<sub>ξ</sub>(χ). Par conséquent, si la puissance
ℵ<sub>ξ</sub>(χ) est indépendante du point x de l'espace considéré, nous
pouvons écrire la topologie dans l'espace par le mot de la conver,
gence d'un système ordonné de la puissance ℵ<sub>ξ</sub>. Ainsi, on peut dire
que l'espace jouit en un sens de la structure uniforme par rapport à
la limite.
De plus, quoiqu'un espace considéré R ne soit pas à structure
uniforlne en ce sens enoncé plus haut, s'il est quantitatif, la puissance
d'ensemble de suffixes de voisinages est indépendante de points
de l'espace et, par suite, on peut considérer que l'espace est à structure
unifonne par rapport à la lilnite. Ainsi, il sera naturel que,
dans l'espace quantitatif, la notion ayant des relations avec une puissance
doit être définie en relation avec la puissance de 1'ensemble
des suffixes, et, en effet, on pourra voir dans § 5 que la puissance
joura un rôle important dans tel espace.
Dans ce travail, nous traitons principalement pour abréger les
espaces quantitatifs dans lesquels chaque voisinage est ouvert. Le
premier objet de cet article est d'excepter des notions ayant des
relations avec la puissance ℵ<sub>0</sub> dans le sens conventionnel, et le
deuxième, de démontrer un traitement naturel sur quelques affaires
fondaInentales dans la topologie. Nous traiterons les espaces quantitatifs
dans § 5 et les espaces à structure uniforme dans § 6.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Sur un Ensemble De Capacité Nulle et L'infini D'un PotentielENNobuyukiNinomiyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566221953Quelques Généralisations des Théorémes Concernant aux Produits Directs Des Espaces Linéaires Localement ConvexesENIchiroAmemiya<p>Les deux théorèmes, qui sont établis dans "Sur les espaces
linéaires localement convexes" par O. Takenouchi (qui a paru dans
ce même Journal, tom. 2, n°1, pp. 57-84), et qui insistent que le
produit direct des espaces de chacune de deux espèces c.-à-d. "bornologique"
et "tonnelé" est encore l'un de la même espèce, sont
vrais sous les conditions moins restrictives. À savoir,
Concernant au théorème 14: La restriction d'être complet n'est
pas nécessaire.
Concernant au théorème 15: La puissance d'ensemble des composants
du produit peut être tenue encore plus grand.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952On Families of Continuous Vector Fields Over SpheresENMasahiroSugawaraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Sur les Espaces Lineaires Localement ConvexesENOsamuTakenouchiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952On the Cartan Invariants of AlgebrasENMasaruOsimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Eine Notwendige Bedingung für die Gültigkeit der Klassenkörpertheorie 1M KleinenENMikaoMoriyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952On The Spaces With Normal Projective Connexions And Some Imbedding Problem Of Riemannian Spaces IIENTominosukeOtsuki<p>In the present paper, we shall investigate the conditions under
which a given Riemannian space V<sub>n</sub> can be imbedded, as a hypersurface,
into a Riemannian space V<sub>n+1</sub> which has the following properties
I) and II).
I) The group of holonomy of the space with a normal projective
.connexion corresponding to V<sub>n+1</sub> fixes a hyperquadric and V<sub>n</sub> is its
image in V<sub>n+1</sub> , that is, the locus of points lying on the parallel displaced
hyperquadrics, regarded as points in the tangent projective spaces.
If V<sub>n+1</sub> has the property above, there exist a scalar y such that
the hypersurface is given by the relation y -= 0.
II) The orthogonal trajectories of the family of the hypersurfaces
on which y is constant are geodesics in V<sub>n+1</sub>.
If the group of holonomy of the space with a normal projective
eonnexion corresponding to a V<sub>n+1</sub> fixes a hyperquadric, it is projectively
equivalent to an Einstein space2
). In the previous paper,
the author have studied the problem of the same kind as this under
the conditions I) and
II') V<sub>n+1</sub> is an Einstein space.
The imbedding problem of V<sub>n</sub> into V<sub>n+1</sub> under the only condition
I) is very complicated in structure. The purpose of the present paper
is also to search for the methods dealing with the problem, as the previous one.
</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Sur Une Suite Convergente de Distributions de Masses et Leurs Potentiels CorrespondantsENNobuyukiNinomiyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Compactification of Topological SpacesENTakashiInagakiMasahiroSugawaraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566211952Sur le Caractére Fonctionelle de la Solution du Probléme de DirichletENNobuyukiNinomiyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Some remarks on radical idealsENHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954On the regularly convex hull of a set in a conjugate Banach spaceENMinoruTomitaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Some studies on Frobenius algebras, IIENMasaruOsimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Sur les anneaux des fonctions continues à support compactENKaichiroFujiwaraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Notes on basic rings, IIENMasaruOsimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Some remarks on homotopy groups of rotation groupsENMasahiroSugawaraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954A construction of closed surfaces of negative curvature in E^4ENTominosukeOtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Representations of operator algebrasENMinoruTomitaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566321954Supplement to my previous paper "On primary ideal decompositions in non-commutative rings"ENHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On primary ideal decompositions in non-commutative ringsENHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On the induced characters of groups of finite orderENMasaruOsimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Necessary conditions for local class field theoryENO. F. G.SchillingNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Some theorems on a system of matrices and a geometrical applicationENTominosukeOtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On the homotopy groups of rotation groupsENMasahiroSugawaraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Inverses in Euclidean mobsENA. D.WallaceNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Indecomposable semigroupsENA. D.WallaceNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953On some Riemann spacesENTominosukeOtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-1566311953Charakterisierung der nicht-archimedischen Bewertungen durch GrössenordnungenENMikaoMoriyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994The Atiyah-Singer Index Theorem for G-Equivariant Real Elliptic FamiliesENKenjiTsuboiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Anti-Integral Extensions and Unramified ExtensionsENMitsuoKanemitsuKen-ichiYoshidaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994On R-Automorphisms of R[X]ENMiguelFerreroAntonioPaquesNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994On Some Products of β-Elements in the Homotopy of the Moore Spectrum IIENHiromiInoueYoshikoOsakadaKatsumiSimomuraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994The Element \bar{kappa} is not in the Image of the S¹-TransferENJunoMukaiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994A Generalization of the Bott-Taubes Rigidity TheoremENShuichiTsukudaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994On commutative group algebras. IIENKaoruMotoseNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Structure of Rings Satisfying Certain Polynomial Identities and Commutativity TheoremsENIsaoMogamiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Note on the Generalized Euler ConstantsENTakashiTasakaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Theta Functions. IENTakashiTasakaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994A Note on the K-Theory of Constructible Sheves over a CurveENTetsuoSasakiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Finite p-groups with cyclic subgroups of index p²ENYasushiNinomiyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994Structure of Semiprime Rings Satisfying Certain ConditionsENTsunekazuNishinakaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994TTF-Theory Over a Semiperfect RingENShojiMorimotoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663611994An Integral Involving the Error Term of the Mean Square of the Riemann Zeta-Function in the Critical StripENIsaoKiuchiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009MULTIPLE POISSON KERNELSENMauroSpreaficoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009A NOTE ON ALMOST INJECTIVE MODULESENAdelAlahmadiSurender K.Jain<p>We give some new properties of almost injective modules and their endomorphism rings, and also provide conditions as to when a direct sum of almost injective (or CS) modules is again almost injective (or CS) in some special cases..</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON LIE IDEALS AND LEFT JORDAN σ-CENTRALIZERS OF 2-TORSION-FREE RINGSENWagnerCortesClausHaetinger<p>B. Zalar proved that any left (resp. right) Jordan centralizer on a 2-torsion-free semiprime ring is a left (resp. right) centralizer. We prove this question changing the semiprimality condition on R. The main result of this paper is the following. Let R be a 2-torsionfree ring which has a commutator right (resp. left) nonzero divisor and
let G: R → R be left (resp. right) Jordan σ-centralizer mapping of , where σ is an automorphism of R. Then G is a left (resp. right) -centralizer mapping of R.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009A NOTE ON CERTAIN METRICS ON R<sup>4</sup><sub>+</sub>ENTominosukeOtsukiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009LOCALLY AND COLOCALLY FACTORABLE BANACH SPACESENF. B.H.JamjoomH. M.Jebreen<p>We generalize the concept of locality (resp. colocality) to the concept of locally factorable (resp. colocally factorable) such that Theorem 2 of [2] and Theorems 1.7 and 1.16 of [11] are still valid for the new concepts. In addition we show that locally factorable and colocally factorable are inherited by complemented subspace, then we present some examples and establish relations between locally factorable and colocally factorable. We prove some relations between being finitely (resp. cofinitely) represented in a Banach space and being locally factorable (resp. colocally factorable) some family of finite dimensional Banach spaces.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009RADIAL HEAT OPERATORS ON JACOBI-LIKE FORMSENMinHoLEE<p>We consider a differential operator D<sup>X</sup> <sub>λ</sub> associated to an
integer λ acting on the space of formal power series, which may be
regarded as the heat operator with respect to the radial coordinate in the 2λ-dimensional space for λ > 0. We show that D<sup>X</sup> <sub>λ</sub> carries Jacobilike
forms of weight λ to ones of weight λ+2 and obtain the formula for the m-fold composite (D<sup>X</sup> <sub>λ</sub> )<sup>[m]</sup> of such operators. We then determine the
corresponding operators on modular series and as well as on automorphic pseudodifferential operators.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON THE JORDAN DECOMPOSITION OF TENSORED MATRICES OF JORDAN CANONICAL FORMSENKei-ichiroIimaRyoIwamatsu<p>Let κ be an algebraically closed field of characteristic p ≥ 0. We shall consider the problem of finding out a Jordan canonical form of
J(α , s)⊗<sub>κ</sub>J(β , t), where J(α, s) means the Jordan block with eigenvalue
α ∈ κ and size s.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON ι-ADIC ITERATED INTEGRALS, IV -Ramification and generators of Galois actions on fundamental groups and torsors of pathsENZdzislawWojtkowiak<p>We are studying Galois representations on fundamental groups and on torsors of paths of a projective line minus a finite number of points. We reprove by explicit calculations some known results about
ramification properties of such representations. We calculate the number
of generators in degree 1 of the images of these Galois representations. We show also that the number of linearly independent generators in degree greater than 1 is equal &franc12 φ(n) for the action of G<sub>Q(μ5)</sub> on the fundamental group of P<sup>1</sup><sub>¯Q</sub>
\ ({0,∞} ∪ μ<sub>n</sub>). Finally we show that the graded Lie algebra associated with the action of G<sub>Q(μ5)</sub> on the fundamental
group of P<sup>1</sup><sub>¯Q</sub>
\ ({0,∞} ∪ μ<sub>5</sub>) is not free.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009LINKAGE AND DUALITY OF MODULESENKenjiNishida<p>Martsinkovsky and Strooker [13] recently introduced module theoretic linkage using syzygy and transpose. This generalization brings possibility of much application of linkage, especially, to homological
theory of modules. In the present paper, we connect linkage of modules to certain duality of modules. We deal with Gorenstein dimension, Cohen-Macaulay modules over a Gorenstein local ring using linkage and generalize the results to non-commutative algebras.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009COMMUTATIVE GROUP ALGEBRAS OF ABELIAN GROUPS WITH UNCOUNTABLE POWERS AND LENGTHSENPeterDanchev<p>Let F be a field of char(F) = p > 0 and G an abelian group
with p-component G<sub>p</sub> of cardinality at most ℵ<sub>1</sub> and length at most ω<sub>1</sub>. The main affirmation on the Direct Factor Problem is that S(FG)/G<sub>p</sub> is totally projective whenever F is perfect. This extends results due to May (Contemp. Math., 1989) and Hill-Ullery (Proc. Amer. Math. Soc., 1990). As applications to the Isomorphism Problem, suppose that for any group H the F-isomorphism FH ≅ FG holds. Then if G<sub>p</sub> is totally projective, H<sub>p</sub> ≅ G<sub>p</sub>. This partially solves a problem posed by May (Proc. Amer. Math. Soc., 1988). In particular, H ≅ G provided G is
p-mixed of torsion-free rank one so that G<sub>p</sub> is totally projective. The same isomorphism H ≅ G is fulfilled when G is p-local algebraically compact too. Besides if F<sub>p</sub> is the simple field with p-elements and G<sub>p</sub> F<sub>p</sub>H
is a coproduct of torsion complete groups, F<sub>p</sub>H ≅ F<sub>p</sub>G as F<sub>p</sub> F<sub>p</sub>-algebras implies H<sub>p</sub> ≅ G<sub>p</sub>. This expands the central theorem obtained by us in (Rend. Sem. Mat. Univ. Padova, 1999) and partly settles the generalized version of a question raised by May (Proc. Amer. Math. Soc.,1979) as well. As a consequence, when G<sub>p</sub> is torsion complete and G is p-mixed of torsion-free rank one, H ≅ G. Moreover, if G is a coproduct of p-local algebraically compact groups then H ≅ G. The last
attainment enlarges an assertion of Beers-Richman-Walker (Rend. Sem. Mat. Univ. Padova, 1983).
Each of the reported achievements strengthens our statements in this direction (Southeast Asian Bull. Math., 2001-2002) and also continues own studies in this aspect (Hokkaido Math. J., 2000) and (Kyungpook Math. J., 2004).</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009ON THE FUNDAMENTAL GROUPS OF LOG CONFIGURATION SCHEMESENYuichiroHoshi<p>In the present paper, we study the cuspidalization problem for the fundamental group of a curve by means of the log geometry of the log configuration scheme, which is a natural compactification of the usual configuration space of the curve. The goal of this paper is to show
that the fundamental group of the configuration space is generated by the images from morphisms from a group extension of the fundamental groups of the configuration spaces of lower dimension, and that the fundamental group of the configuration space can be partially reconstructed from a collection of data concerning the fundamental groups of the configuration spaces of lower dimension.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009THE SPACE L<sub>q</sub> OF DOUBLE SEQUENCESENFeyziBasarYurdalSever<p>The spaces BS, BS(t), CS<sub>p</sub>, CS<sub>bp</sub>, CS<sub>r</sub> and BV of double
sequences have recently been studied by Altay and Ba¸sar [J. Math. Anal. Appl. 309(1)(2005), 70–90]. In this work, following Altay and Ba¸sar [1], we introduce the Banach space L<sub>q</sub> of double sequences corresponding to the well-known space ℓ<sub>q</sub> of single sequences and examine some properties
of the space L<sub>q</sub>. Furthermore, we determine the β(υ)-dual of the space
and establish that the α- and γ-duals of the space L<sub>q</sub> coincide with the β(υ)-dual; where 1 ≤ q < ∞ and υ 2 {p, bp, r}.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009SOME IDENTITIES RELATING MOCK THETA FUNCTIONS WHICH ARE DERIVED FROM DENOMINATOR IDENTITYENYukariSanada<p>We show that there exists a new connection between identities satisfied by mock theta functions and special case of denominator identities for affine Lie superalgebras.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665112009NAKAYAMA ISOMORPHISMS FOR THE MAXIMAL QUOTIENT RING OF A LEFT HARADA RINGENKazuakiNonomura<p>From several results of Kado and Oshiro, we see that if
the maximal quotient ring of a given left Harada ring R of type (*) has a Nakayama automorphism, then R has a Nakayama isomorphism. This result poses a question whether if the maximal quotient ring of a given left Harada ring R has a Nakayama isomorphism, then R has a
Nakayama isomorphism. In this paper, we shall show that a basic ring of the maximal quotient ring of a given Harada ring has a Nakayama isomorphism if and only if its Harada ring has a Nakayama isomorphism.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989C-Totally Real Submanifolds of S^7(1) with Non-Negative Sectional CurvatureENFrankiDillenLucVranckenNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Some Generalizations of Boolean RingsENHiroakiOkamotoJulieGrosenHiroakiKomatsuNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Commutative Rings over which all Semiprime Finitely Generated Algebras are SeparableENYasuyukiHiranoJae KeolParkNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Galois H-Dimodule AlgebrasENKarl-H.UlbrichNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Hereditary Artinian Rings and Azumaya's Exactness ConditionENKent R.FullerWeiminXueNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Some Decomposition Theorems for RingsENHiroakiKomatsuHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Tauberian Theorems of Jp → Mp-TypeENHubertTietzNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Harada Rings. IIENKiyoichiOshiroNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Separated Sets of Torsion TheoriesENJonathan S.GolanNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Some Results on the Weak Normalization of an Integral DomainENDavid E.DobbsMarcoFontanaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Some Decomposition Theorems for Periodic Rings and Near-RingsENHoward E.BellSteveLighNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Generalized PF-RingsENHasanAl-EzehNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Primitive Elements of Galois Extensions of Commutative Semi-Local RingsENIsaoKikumasaTakasiNagaharaKazuoKishimotoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989The Distribution of Pythagorean Triples and a Three-Dimensional Divisor ProblemENWerner GeorgNowakWinfriedRecknagelNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Zur Struktur Nichtkommutativer RingeENWalterStrebNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Harada Rings. IENKiyoichiOshiroNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Sets Which Contain a Quadratic Residue Modulo p for Almost All pENMichael A.FilasetaDavid R.RichmanNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Chacron's Condition and Commutativity TheoremsENHiroakiKomatsuHisaoTominagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989A Note on Fixed RingsENYoshimiKitamuraNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989Asymptotic Behavior of a Certain Multiplicative FunctionENIsaoKiuchiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On Primitive Elements of Galois Extensions of Commutative Semi-Local Rings IIENIsaoKikumasaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989On H-Rings with Homogeneous SoclesENKiyoichiOshiroKazuoShigenagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15663111989The A-Cohomology of the Stunted Quaternionic (Quasi-)projective SpacesENMitsunoriImaokaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Skew Group Algebras and their Yoneda Algebras ENRobertoMartinez-villa<p>Skew group algebras appear in connection with the study
of singularities [1], [2]. It was proved in [4], [6], [10] the preprojective algebra of an Euclidean diagram is Morita equivalent to a skew group algebra of a polynomial algebra. In [7] we investigated the Yoneda algebra
of a selfinjective Koszul algebra and proved they have properties analogous to the commutative regular algebras, we call such algebras generalized Auslander regular. The aim of the paper is to prove that given a positively graded locally finite K-algebra Λ = ∑ί≥0
Λ<sub>ί</sub> and a finite grading preserving group G of automorphisms of Λ, with characteristic K not dividing the order of G, then G acts naturally on the Yoneda algebra Γ =⊕κ≥0　Ext<sup>k</sup><sub>Λ</sub>(Λ0,Λ0) and the skew group algebra Γ*G is isomorphic
to the Yoneda algebra Λ*G = ⊕κ≥0 Ext<sup>κ</sup><sub>Λ</sub>*<sub>G</sub>(Λ0*G,Λ0*G). As an application we prove Λ is generalized Auslander regular if and only if Λ*G is generalized Auslander regular and Λ is Koszul if and only if
Λ*G is so.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Nonlinear Ergodic Theorems for Semigroups of Non-Lipschitzian Mappings in Banach Spaces II ENIsaoMiyadera<p>Let C be a nonempty closed convex subset of a uniformly
convex Banach space, and let S = {T(t); t ≥ 0} be a nonlinear semigroup of non-Lipschitzian mappings on C which is asymptotically nonexpansive in the intermediate sense. In this paper we study weak almost
convergence of almost-orbits of S.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001The Role of Commutators in a Non-Cancellation Phenomenon ENTomas EdsonBarrosAlcibiadesRigas<p>We construct an explicit (from the transition function point of view) diffeomorphism between the cartesian products with the 3-sphere of two 10-dimensional loop spaces that are not homotopy equivalent to each other. Our method employs specific models for some S<sup>3</sup>-
principal bundles over S<sup>7</sup> and relates the study of this type of noncancellation phenomena to commutators of groups. Our formulas depend only on specifying homotopies of powers of commutators to constants.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Configuration Spaces with Partially Summable Labels and Homology Theories ENKazuhisaShimakawa<p>It is shown that any subset of a topological abelian monoid gives rise to a generalized homology theory that is closely related to the notion of labeled configuration space. Applications of the main theorem include generalizations of the classical Dold-Thom and the Barratt-
Priddy-Quillen-Segal theorems.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001On the Extensions of Single Valued Continuous and Set Valued Usc Maps ENShogoIkenagaShin-ichiNittaIwaoYoshioka<p>We show that two main theorems: (1) A regular space Y
has a complete sequence if and only if the set valued usco map to Y defined on every dense set D of any space X has an usco extension over a Gδ-set in X containing D. (2) A regular space Y with a Gδ-diagonal has a complete sequence if and only if the single valued continuous map to Y defined on every dense set D of any space X has a continuous extension over a Gδ-set in X containing D.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Some Cohomotopy Groups of Suspended Projective Planes ENHideyukiKachiJunoMukaiT.NozakiY.SumitaD.Tamaki<p>In this paper we compute some cohomotopy groups of the
suspended complex and quaternionic projective plane by use of the exact sequence associated with the canonical cofiber sequence and a formula about a multiple of the identity class of the suspended projective plane.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Real Embeddings of Real Projective Curves and Real Ramification Points ENEdoardoBallico<p>Here we study real immersions in a projective space of
smooth projective curves defined over R but without real ramification points, giving several examples for canonical embeddings (i.e. existence of real curves without real Weierstrass points) and for plane curves. We also gives numerical obstructions to the existence of real morphisms
without real ramification points.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Certain Metrics on R<sup>4</sup>+(Ⅱ)ENTominosukeOtsuki<p>This paper is a continuation of the one with the same title([4]), in which we obtained a special solution for a system of differential equations on metric tensors on R<sup>4</sup>+ satisfying the Einstein condition for Case I generalizing the Ot-metric:
in Theorem 1, and proved that there exist no solutions for Case II in Theorem 2. In this work, we shall show that we can obtain more general solutions for Case I which depend on the latitude parameter. We use the results in [4], so the section numbers start from 5.
1. Preliminaries and curvature tensor
2. Ricci tensor
3. Solutions for Case I
4. Analysis and a conclusion for Case II</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Adjoint Orbit Types of Compact Exceptional Lie Group G<sub>2</sub> in its Lie Algebra ENTakashiMiyasakaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664312001Stable Module Theory with Kernels ENKirikoKatoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987An extension of a theorem of D. Gromoll and J. A. WolfENNobuhiroInnamiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On Morita pairs of ringsENNobuoNobusawaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987Primitive elements of cyclic extensions of commutative ringsENIsaoKikumasaTakasiNagaharaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On H-separable extensions in Azumaya algebrasENHiroakiOkamotoHiroakiKomatsuShûichiIkehataNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On the complement class to the torsion theoryENKazuoShigenagaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987Closed ideals in non-unital matrix ringsENShojiKyunoMi-Soo B.SmithNobuoNobusawaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On the KO-cohomologies of the stunted lens spacesENAkieTamamuraSusumuKônoNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987Rings satisfying the identity (X-X^n)(Y-Y^n) = 0ENYasuyukiHiranoAdilYaqubNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987(σ,τ)-derivations in prime ringsENNurcanArgaçArifKayaAlevKisirNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On the Loewy structure of the projective indecomposable modules for a 3-solvable group IENYasushiNinomiyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987Radicals of skew polynomial rings and skew Laurent polynomial ringsENMiguelFerreroNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On the Loewy structure of the projective indecomposable modules for a 3-solvable group IIENYasushiNinomiyaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On cohomology of groups in finite local ringsENTakaoSumiyamaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On some properties of Gaussian covariance operators in Banach spacesENYasujiTakahashiYoshiakiOkazakiNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On the double centralizer of the injective hull relative to a torsion theoryENYoshikiKurataMing-TingChenNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987Some periodicity conditions for ringsENHoward E.BellAdilYaqubNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On SD graphs. IENNoboruItoMachioTadokoroNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On artinian rings of right local typeENTakeshiSumiokaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On Hopf Galois extensions, Azumaya algebras and skew polynomial ringsENAtsushiNakajimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987The Taylor coefficients of ζ(s),(s-1)ζ(s) and (z/(1-z))ζ(1/(1-z))ENMasumiNakajimaNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15662911987On the higher derivations of communitive ringsENSadiAbu-SaymehMasatoshiIkedaNo potential conflict of interest relevant to this article was reported.