Some results on irreducible ideals of monoids

TL;DR

This paper investigates algebraic properties of irreducible ideals in monoids, establishing relationships with prime and semiprime ideals and exploring their characteristics in specific classes of monoids.

Contribution

It provides new insights into the structure of irreducible ideals in monoids and their connections to other ideal types, expanding understanding in algebraic monoid theory.

Findings

Relations between irreducible, prime, and semiprime ideals established

Properties of irreducible ideals in local monoids analyzed

Characteristics of irreducible ideals in Noetherian and Laskerian monoids explored

Abstract

The purpose of this note is to study some algebraic properties of irreducible ideals of monoids. We establish relations between irreducible, prime, and semiprime ideals. We explore some properties of irreducible ideals in local, Noetherian, and Laskerian monoids.