On Rees matrix semigroups M(S;I,Λ;P) over semigroups S in which I is a singleton

Abstract

Let M ( S ; Λ ; P ) denote a Rees I × Λ matrix semigroup over a semigroup S in which I is a singleton. In this paper we describe the right regular representation of M ( S ; Λ ; P ) , and find connection between properties of S and M ( S ; Λ ; P ) . We also prove embedding theorems on Rees matrix semigroups M ( S ; Λ ; P ) .