Right regular triples of semigroups

TL;DR

This paper investigates the structure of right regular triples of semigroups, focusing on Rees matrix semigroups and their kernels, to understand their algebraic properties and classifications.

Contribution

It introduces the concept of right regular triples of semigroups and analyzes their structure through Rees matrix semigroups and kernel isomorphisms.

Findings

Characterization of right regular triples via Rees matrix semigroups

Conditions for isomorphism between quotient semigroups

Structural insights into kernels of right regular triples

Abstract

Let ${\cal M}(S; \Lambda; P)$ 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 $A\stackrel{P}{\longleftarrow}B$ and $B\stackrel{P'}{\longrightarrow}C$ such that ${\cal M}(A; B; P)/\theta_{{\cal M}(A; B; P)}\cong {\cal M}(C; B; P')$. In this paper we examine right regular triples of semigroups.