دوره 10، شماره 1 - ( 1-1394 )
جلد 10 شماره 1 صفحات 137-131 |
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Payrovi S, Babaei S. On the 2-absorbing Submodules. IJMSI 2015; 10 (1) :131-137
URL: http://ijmsi.ir/article-1-512-fa.html
URL: http://ijmsi.ir/article-1-512-fa.html
On the 2-absorbing Submodules. مجله علوم ریاضی و انفورماتیک. 1394; 10 (1) :131-137
چکیده:
Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of $M$ and $M/N$ is Noetherian, then a chain of 2-absorbing submodules of $M$ is constructed. Furthermore, the annihilation of $E(R/frak p)$ is studied whenever $0$ is a 2-absorbing submodule of $E(R/frak p)$, where $frak p$ is a prime ideal of $R$ and $E(R/frak p)$ is an injective envelope of $R/frak p$.
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