Classification of interior ideals in regular and intra regular semigroups

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