International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 507-520
doi: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 Yue-Chan Phoebe Ho. 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=B∪C∪{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.