Classification of interior ideals in regular and intra regular semigroups

Abstract

This paper delves into the classification of regular semigroups and their various subclassifications based on their interior ideals. By introducing and examining concepts such as strongly prime, prime, semiprime, strongly irreducible, and irreducible interior ideals, we present a new framework for understanding regular semigroups. In addition, we investigate the relationships among these different types of ideals, offering a thorough exploration of their interconnections.