On (m,n)-quasi-gamma-ideals in ordered la-gamma-semigroups

Abstract

In this paper, we introduce the concepts of m-left-Γ-ideals, n-right-Γ-ideals and (m,n)-quasi-Γ-ideals in ordered LA-Γ-semigroups and investigate about some properties of those ideals. We show that the intersection of an m-left-Γ-ideal and an n-right-Γ-ideal of an ordered LA-Γ-semigroup is an (m,n)-quasi-Γ-ideal. In addition, we introduce the notion of the (m,n) intersection property in ordered LA-Γ-semigroups and prove that every (m,n)-quasi-Γ-ideal in an ordered LA-Γ-semigroup with left identity has the (m,n) intersection property.