start-ver=1.4 cd-journal=joma no-vol=48 cd-vols= no-issue=1 article-no= start-page= end-page= dt-received= dt-revised= dt-accepted= dt-pub-year=2006 dt-pub=200601 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Stickelberger Ideals and Normal Bases of Rings of p-integers en-subtitle= kn-subtitle= en-abstract= kn-abstract= en-copyright= kn-copyright= en-aut-name=IchimuraHumio en-aut-sei=Ichimura en-aut-mei=Humio kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Ibaraki University END start-ver=1.4 cd-journal=joma no-vol=54 cd-vols= no-issue=1 article-no= start-page=33 end-page=48 dt-received= dt-revised= dt-accepted= dt-pub-year=2012 dt-pub=201201 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=HILBERT-SPEISER NUMBER FIELDS AND STICKELBERGER IDEALS; THE CASE p = 2 en-subtitle= kn-subtitle= en-abstract= kn-abstract=We say that a number field F satisfies the condition (H′2m) when any abelian extension of exponent dividing 2m has a normal basis with respect to rings of 2-integers. We say that it satisfies (H′ 2) when it satisfies (H′ 2m) for all m. We give a condition for F to satisfy (H'2m), and show that the imaginary quadratic fields F = Q(√−1) and Q(√−2) satisfy the very strong condition (H′ 2) if the conjecture that h+2m = 1 for all m is valid. Here, h+2m) is the class number of the maximal real abelian field of conductor 2m. en-copyright= kn-copyright= en-aut-name=IchimuraHumio en-aut-sei=Ichimura en-aut-mei=Humio kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Faculty of Science, Ibaraki University en-keyword=Hilbert-Speiser number field kn-keyword=Hilbert-Speiser number field en-keyword=Stickelberger ideal kn-keyword=Stickelberger ideal en-keyword=normal integral basis kn-keyword=normal integral basis END start-ver=1.4 cd-journal=joma no-vol=58 cd-vols= no-issue=1 article-no= start-page=125 end-page=132 dt-received= dt-revised= dt-accepted= dt-pub-year=2016 dt-pub=201601 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=On a duality of Gras between totally positive and primary cyclotomic units en-subtitle= kn-subtitle= en-abstract= kn-abstract=Let K be a real abelian field of odd degree over Q, and C the group of cyclotomic units of K. We denote by C+ and C0 the totally positive and primary elements of C, respectively. G. Gras found a duality between the Galois modules C+/C2 and C0/C2 by some ingenious calculation on cyclotomic units. We give an alternative proof using a consequence (=“Gras conjecture”) of the Iwasawa main conjecture and the standard reflection argument. We also give some related topics. en-copyright= kn-copyright= en-aut-name=IchimuraHumio en-aut-sei=Ichimura en-aut-mei=Humio kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Faculty of Science, Ibaraki University en-keyword=cyclotomic units kn-keyword=cyclotomic units en-keyword=reflection argument kn-keyword=reflection argument en-keyword=ideal class group kn-keyword=ideal class group END