On disjunctions of algebraic sets in completely simple semigroups

TL;DR

This paper investigates the conditions under which completely simple semigroups are equational domains, meaning finite unions of algebraic sets are algebraic, thereby advancing the understanding of algebraic structures in semigroup theory.

Contribution

It provides necessary and sufficient conditions characterizing when completely simple semigroups are equational domains, a novel contribution to algebraic semigroup theory.

Findings

Identifies conditions for completely simple semigroups to be equational domains

Establishes criteria for algebraic sets in semigroup unions

Advances theoretical understanding of algebraic structures in semigroups

Abstract

A semigroup $S$ is called an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove some necessary and sufficient conditions for a completely simple semigroup to be an equational domain.