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International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 507-520
http://dx.doi.org/10.1155/S0161171296000713

On completely 0-simple semigroups

Department of Mathematics and Computer Science, Central Missouri State University, Warrensburg 64093, MO, USA

Received 17 March 1994; Revised 31 August 1995

Copyright © 1996 Hindawi Publishing Corporation. 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.

Abstract

Let S be a completely 0-simple semigroup and F be an algebraically closed field. Then for each 0-minimal right ideal M of S, M=BC{0}, where B is a right group and C is a zero semigroup. Also, a matrix representation for S other than Rees matrix is found for the condition that the semigroup ring R(F,S) is semisimple Artinian.