Bulletin of the
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Bull. Korean Math. Soc. 2021; 58(6): 1507-1520

Published online November 30, 2021 https://doi.org/10.4134/BKMS.b210005

Copyright © The Korean Mathematical Society.

On weakly quasi $n$-absorbing submodules

Mohammed Issoual, Najib Mahdou, Moutu Abdou Salam Moutui

University S.M. Ben Abdellah Fez; University S.M. Ben Abdellah Fez; 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: Primary 13A15, 13B02

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