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.