ID  33138 
FullText URL  
Author 
Chikunji, Chiteng'a John

Abstract  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 Romodules. Let nonnegative 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. 
Keywords  unit groups
completely primary finite rings
galois rings

Published Date  200801

Publication Title 
Mathematical Journal of Okayama University

Volume  volume50

Issue  issue1

Publisher  Department of Mathematics, Faculty of Science, Okayama University

ISSN  00301566

NCID  AA00723502

Content Type 
Journal Article

language 
英語

File Version  publisher

Refereed 
True

Submission Path  mjou/vol50/iss1/8
