Tri-Quasi Ideals of Γ-Semirings

Abstract

Abstract In this paper, as a further generalization of ideals, we introduce the notion of tri-quasi ideal as a generalization of ideal, left ideal, right ideal, bi-ideal, quasi ideal, interior ideal, bi-interior ideal,weak interior ideal, bi-quasi ideal, tri-ideal,quasi-interior ideal and bi-quasi-interior ideal of Γ-semiring. Some charecterizations of Γ-semiring,regular Γ-semiring and simple Γ-semiring using tri-quasi ideals are given and study the properties of tri-quasi ideals of Γ-semiring.