Soft Intersection Semigroups, Ideals and Bi-Ideals; a New Application on Semigroup Theory I

Abstract

In this paper, we define soft intersection semigroups, soft intersection left (right, two-sided) ideals and bi-ideals of semigroups, give their properties and interrelations and we characterize regular, intra-regular, completely regular, weakly regular and quasi-regular semigroups in terms of these ideals.