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Some properties of graded generalized 2-absorbing submodules

Alghueiri Shatha, Al-Zoubi Khaldoun

Demonstratio Mathematica

2022

Vol. 55, nr 1

343--353

Let G be an abelian group with identity e . Let R be a G -graded commutative ring and M a graded R -module. In this paper, we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous components. Special attention has been paid, when graded rings are graded gr-Noetherian, to find extra properties of these graded submodules.

On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings

Al-Zoubi Khaldoun, Alghueiri Shatha

Demonstratio Mathematica

2021

Vol. 54, nr 1

162--167

Let G be an abelian group with identitye. Let R be a G-graded commutative ring with identity 1, and M be a graded R-module. In this paper, we introduce the concept of graded Jgr-classical 2-absorbing submodule as a generalization of a graded classical 2-absorbing submodule. We give some results concerningof these classes of graded submodules. A proper graded submodule C of M is called a graded Jgr-classical 2-absorbing submodule of M, if whenever rg, sh, ti ∈ h(R) and xj ∈ h(M) with rgshtixj ∈ C, then either rgshxj ∈ C + Jgr(M) or rgtixj ∈ C + Jgr(M) or shtixj ∈ C + Jgr(M), where Jgr(M) is the graded Jacobson radical.