Generalizations of graded S-primary ideals

Abstract

The goal of this article is to present the graded weakly S-primary ideals and graded g-weakly S-primary ideals which are extensions of graded weakly primary ideals. We state P is a graded weakly S-primary ideal of R if there exists s ∈ S such that for all x, y ∈ h(R), if 0 6=xy ∈ P, then sx ∈ P or sy ∈ Grad(P). Several properties and characteristics of graded weakly S-primary ideals as well as graded g-weakly S-primary ideals are investigated.