On Commutative Monoid Congruences of Semigroups

TL;DR

This paper explores how medial subsets of a semigroup can be used to construct commutative monoid congruences, providing a new approach to understanding the algebraic structure of semigroups.

Contribution

It introduces a method to construct commutative monoid congruences of semigroups using medial subsets, offering a novel perspective in algebraic theory.

Findings

Medial subsets characterize certain congruences in semigroups.

A construction method for commutative monoid congruences is provided.

The approach links medial subsets to algebraic structure analysis.

Abstract

A subset A of a semigroup S is called a medial subset of S if xaby is in A if and only if xbay is in A for every elements x, y, a, b of S. In the paper we show how we can construct the commutative monoid congruences of a semigroup S by the help of medial subsets of S.