ID | 33138 |
フルテキストURL | |
著者 |
Chikunji, Chiteng'a John
Botswana College
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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
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発行日 | 2008-01
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出版物タイトル |
Mathematical Journal of Okayama University
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巻 | 50巻
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号 | 1号
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出版者 | Department of Mathematics, Faculty of Science, Okayama University
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開始ページ | 149
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終了ページ | 160
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ISSN | 0030-1566
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NCID | AA00723502
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資料タイプ |
学術雑誌論文
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言語 |
英語
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論文のバージョン | publisher
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査読 |
有り
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Submission Path | mjou/vol50/iss1/8
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JaLCDOI |