On Graded 2-Absorbing Primary and Graded Weakly 2-Absorbing Primary Ideals

Abstract

Abstract. Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study graded 2-absorbing primary and graded weakly 2-absorbing primary ideals of a graded ring which are different from 2-absorbing primary and weakly 2-absorbing primary ideals. We give some properties and characterizations of these ideals and their homogeneous components.

Graded ϕ-2-Absorbing and Graded ϕ-2-Absorbing Primary Submodules

“…Al-Zoubi and Sharafat in [12] proposed the notion of graded 2-absorbing primary ideals, where a proper graded ideal I of R is called graded 2-absorbing primary if whenever x, y, z ∈ h(R) with xyz ∈ I, then xy ∈ I or xz ∈ Grad(I) or yz ∈ Grad(I). The notion of graded 2-absorbing primary submodules is studied in [7] as a generalization of graded 2-absorbing primary ideals.…”

Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary

“…In this case P = Grad(Q) is a graded prime ideal of R, and Q is said to be graded P-primary. In [4], Al-Zoubi and Sharafat introduced a generalization of graded primary ideals called graded 2-absorbing primary ideals. A proper graded ideal I of R is called a graded 2-absorbing primary ideal of R if whenever x, y, z ∈ h(R) and xyz ∈ I, then xy ∈ I or xz ∈ Grad(I) or yz ∈ Grad(I).…”

On Graded 2-Absorbing Coprimary Submodules

“…A proper graded ideal P of R is said to be graded 2-absorbing if whenever a, b, c ∈ h(R) such that abc ∈ P , then either ab ∈ P or ac ∈ P or bc ∈ P . Al-Zoubi and Sharafat in [3], introduced the concept of graded 2-absorbing primary ideals. This concept generalizes both graded primary ideals and graded 2-absorbing ideals.…”