On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings

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Pairote Yiarayong, Manoj Siripitukdet, On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings, Int. J. Anal. Appl., 16 (3) (2018), 400-413.

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Pairote Yiarayong, Manoj Siripitukdet

Abstract

Let $R$ be a commutative ring with identity and let $M$ be a unitary $R$-module. We say that a proper submodule $N$ of $M$ is a weakly $2$-absorbing semi-primary submodule if $a_{1}, a_{2}\in R, m\in N$ with $0 \neq a_{1}a_{2}m \in N$, then $a_{1}a_{2}\in \sqrt{(N : M)}$ or $a_{1}m \in N$ or $a^{n}_{2}m\in N$ for some positive integer $n$. In this paper, we study weakly $2$-absorbing semi-primary submodules and we prove some basic properties of these submodules. Also, we give a characterization of weakly $2$-absorbing semi-primary submodules and we investigate weakly $2$-absorbing semi-primary submodules of some well-known modules.

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