A new approach to semigroup theory I: soft union semigroups, ideals and bi-ideals

Abstract

In this paper, soft union semigroups, soft union left (right, two-sided) ideals and bi-ideals of semigroups are defined, their properties and interrelations are given and regular, intra-regular, completely regular, weakly regular and quasi-regular semigroups are characterized in terms of these ideals. This paper is a new approach to classical semigroup theory via soft set theory.