On Monoid Congruences of Commutative Semigroups

TL;DR

This paper characterizes monoid congruences in commutative semigroups using the concept of separators of subsets, providing a construction method for such congruences based on non-empty separators.

Contribution

It introduces a new characterization of monoid congruences in commutative semigroups through the notion of separators of subsets, offering a constructive approach.

Findings

Monoid congruences can be characterized via separators of subsets.

Every monoid congruence can be constructed using subsets with non-empty separators.

The separator concept provides a new tool for analyzing semigroup structures.

Abstract

In this paper we characterize the monoid congruences of commutative semigroups by the help of the notion of the separator of subsets of semigroups. We show that every monoid congruence of a commutative semigroup S can be constructed by the help of subsets A of S whose separator is not empty.