On weakly quasi n-absorbing submodules
Bull. Korean Math. Soc.
Published online June 25, 2021
Mohammed Issoual, Najib Mahdou, and Moutu Abdou Salam Moutui
Sidi Mohamed Ben Abdellah University; Sidi Mohamed Ben Abdellah University; American University of Afghanistan
Abstract : Let $R$ be a commutative ring with $1\neq 0$, $n$ be a positive integer and $M$ be an $R$-module. In this paper, we introduce the concept of weakly quasi $n$-absorbing submodule which is a proper generalization of quasi $n$-absorbing submodule. We define a proper submodule $N$ of $M$ to be a weakly quasi $n$-absorbing submodule if whenever $a\in R$ and $x\in M$ with $0\neq a^{n}x\in N,$ then $a^{n}\in (N:_{R}M)$ or
$a^{n-1}x\in N.$ We study the basic properties of this notion and establish several characterizations.
Keywords : quasi n-absorbing submodule, weakly quasi n-absorbing submodule.
MSC numbers : 13A15,13B02
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