Right regular triples of semigroups

Abstract

Let $\mathcal{M}(S;\Lambda ;P)$ denote a Rees $I\times \Lambda$ matrix semigroup without zero over a semigroup $S$, where $I$ is a singleton. If ${\theta }_S$ denotes the kernel of the right regular representation of a semigroup $S$, then a triple $A,B,C$ of semigroups is said to be right regular, if there are mappings $A\stackrel{P}{⟵}B$ and $B\stackrel{P^{\prime }}{⟶}C$ such that $\mathcal{M}(A;B;P)/{\theta }_{\mathcal{M}(A;B;P)}\cong \mathcal{M}(C;B;P^{\prime })$. In this paper we examine right regular triples of semigroups.

13 pages