Exploring Ideal Structures in Semi groups: A Comparative Study Of Various Classes And Their Properties

Abstract

This article aims to provide a comprehensive investigation into the concept of ideals within various semigroup classes, focusing on their properties, characterization, and role in algebraic structures. The research will cover classical semigroup theories, including regular semigroups, monoids, and groups, as well as less conventional semigroup classes, such as inverse semigroups, transformative semigroups, and idempotent semigroups. By delving into the intricacies of each semigroup type's ideal structures, this work seeks to expand the current understanding of these algebraic structures, offering new insights and potential applications in various fields, such as computer science, mathematics, and theoretical physics.