On graded strongly quasi primary ideals

Abstract

In this article, we introduce graded strongly quasi primary ideals which is an intermediate class of graded primary ideals and graded quasi primary ideals. Let G be a group with identity e, R be a G-graded commutative ring with nonzero unity 1 and P be a proper graded ideal of R. Then P is said to be a graded strongly quasi primary ideal if xy ∈ P for x,y ∈ h(R) implies either x 2 ∈ P or y n ∈ P (x n ∈ P or y 2 ∈ P ) for some n ∈ N. We give many properties of graded strongly quasi primary ideals and investigate the relations between graded strongly quasi primary ideals and other classical graded ideals such as graded primary, graded 2-prime and graded quasi primary ideals