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ID 33599
フルテキストURL
著者
Chikunji, Chiteng’a John University of Transkei
抄録

A completely primary finite ring is a ring R with identity 1 ≠ 0 whose subset of all its zero-divisors forms the unique maximal ideal J. 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(ργ) and the characteristic of R is ργ, where 1 ≤ k ≤ 3, for some prime ρ and positive integer γ. Let Ro = GR(pkr, pk) be a Galois subring of R and let the annihilator of J be J2 so that R = Ro ⊕U ⊕V , where U and V are finitely generated Ro-modules. Let non-gative integers s and t be numbers of elements in the generating sets for U and V , respectively. When s = 2, t = 1 and the characteristic of R is p2 and p3; and when s = 2, t = 2 and the characteristic of R is p, the structure of the group of units R* of the ring R and its generators have been determined; these depend on the structural matrices (alij) and on the parameters p, k, r, s and t.

キーワード
unit groups
completely primary finite rings
galois rings.
発行日
2005-01
出版物タイトル
Mathematical Journal of Okayama University
47巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
開始ページ
39
終了ページ
54
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/vol47/iss1/3
JaLCDOI