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

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) . [ABSTRACT FROM AUTHOR]