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ID 33138
フルテキストURL
著者
Chikunji, Chiteng'a John Botswana College
抄録

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.

キーワード
unit groups
completely primary finite rings
galois rings
発行日
2008-01
出版物タイトル
Mathematical Journal of Okayama University
50巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
言語
English
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol50/iss1/8