International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 579-592
Unit groups of cube radical zero commutative completely primary finite rings
Department of Mathematics, University of Transkei, Private Bag X1, Umtata 5117, South Africa
Received 1 July 2004
Copyright © 2005 Chiteng'a John Chikunji. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A completely primary finite ring is a ring with identity whose subset of all its zero-divisors forms the unique maximal ideal . Let be a commutative completely primary finite ring with the unique maximal ideal such that and . Then and the characteristic of is , where , for some prime and positive integer . Let be a Galois subring of and let the annihilator of be so that , where and are finitely generated -modules. Let nonnegative integers and be numbers of elements in the generating sets for and , respectively. When , , and the characteristic of is ; and when , for any fixed , the structure of the group of units of the ring and its generators are determined; these depend on the structural matrices
and on the parameters , , , and .