Soft intersection semigroups, ideals and bi-ideals; a new application on semigroup theory I

Abstract

In this paper, we dene 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.