Hybrid ideals in ordered semigroups and some characterizations of their regularities

Abstract

The main theme of this present paper is to apply the concept of hybrid structure to study some algebraic properties of ordered semigroups. Indeed, we define the notion of hybrid left (resp., right) ideals in ordered semigroups, and their related properties are investigated. Furthermore, we provide characterizations of regular, intra-regular, and weakly regular ordered semigroups in terms of hybrid left and right ideals.