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

Yiarayong, Pairote; Siripitukdet, Manoj

doi:10.28924/2291-8639-16-2018-400

Research Article

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

Pairote Yiarayong*
Manoj Siripitukdet

* Corresponding author

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.

How to Cite

P. Yiarayong, M. Siripitukdet, On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings, Int. J. Anal. Appl. 16 (2018), 400–413. https://doi.org/10.28924/2291-8639-16-2018-400

BibTeX

@article{Yiarayong2018,
  author  = {Yiarayong, Pairote and Siripitukdet, Manoj},
  title   = {On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {400--413},
  doi     = {10.28924/2291-8639-16-2018-400}
}

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