On the Graded 2-Absorbing Primary Submodules of Graded Multiplication Modules

Fatemeh Soheilnia, Shiroyeh Payrovi

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  • Support Team

Keywords:

Graded 2-absorbing submodule, Graded 2-absorbing primary submodule, Graded multiplication modules

Abstract

Let $G$ be a multiplicative group‎, ‎$R$ be a $G$-graded commutative ring and $M$ be a‎

‎graded $R$-module‎. ‎A proper graded submodule $N$ of $M$ is called graded $2$-absorbing primary‎,

‎if whenever $a,b\in h(R)$ and $m\in h(M)$ with $abm\in N$‎, ‎then $ab\in (N:_R M)$ or‎

‎$am\in Gr_M(N)$ or $bm\in Gr_M(N)$‎. ‎Let $M$ be a graded finitely generated multiplication $R$-module‎.

‎It is shown that $Gr(N‎ :‎_R M) = \big(Gr_M(N)‎ :‎_R M \big)$‎. ‎Furthermore‎, ‎it is proved that $(N‎ :‎_R M)$ is a graded $2$-absorbing primary ideal of $R$‎, ‎if $N$ is a graded $2$-absorbing primary submdoule of $M$‎. ‎Moreover‎, ‎it is generalized some results of graded $2$-absorbing ideals over trivial extension of a ring‎.

 

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Published

2022-06-30

How to Cite

Team, S. (2022). On the Graded 2-Absorbing Primary Submodules of Graded Multiplication Modules : Fatemeh Soheilnia, Shiroyeh Payrovi. Thai Journal of Mathematics, 20(2), 721–728. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1357

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