دوره 20، شماره 1 - ( 1-1404 )
جلد 20 شماره 1 صفحات 110-101 |
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Alghueiri S, Al-Zoubi K. On Graded Semi $J_{gr}$-2-absorbing and Graded Weakly Semi $J_{gr}$-2-absorbing Submodules. IJMSI 2025; 20 (1) :101-110
URL: http://ijmsi.ir/article-1-1847-fa.html
URL: http://ijmsi.ir/article-1-1847-fa.html
On Graded Semi $J_{gr}$-2-absorbing and Graded Weakly Semi $J_{gr}$-2-absorbing Submodules. مجله علوم ریاضی و انفورماتیک. 1404; 20 (1) :101-110
چکیده:
Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concepts of graded semi Jgr-2-absorbing and graded weakly semi Jgr-2-absorbing submodules of M and study the behavior of these notions under several constructions. A proper graded submodule N of M is said to be a graded semi Jgr-2-absorbing (resp. graded weakly semi Jgr-2-absorbing) submodule of M if whenever rg ∈ h(R) and mh ∈ h(M) with rg2mh ∈ N (resp. 0 ≠ rg2mh ∈ N), then either rgmh ∈ N + Jgr(M) or rg2∈ (N + Jgr(M) :R M), where Jgr(M) is the graded Jacobson radical.
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