Korean J. Math. Vol. 28 No. 4 (2020) pp.907-913
DOI: https://doi.org/10.11568/kjm.2020.28.4.907

A characterization of $w$-Artinian modules

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Published: Dec 30, 2020
Keywords:
w-cofinitely generated, w-Artinian module
Mathematics Subject Classification:
13E10, 13D30

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Hwankoo Kim
Department of Mathematics Changwon National University Changwon 51140, Korea
Tae In Kwon
Division of Computer and Information Engineering Hoseo University Asan 31499, Korea
De Chuan Zhou
School of Science Southwest University of Science and Technology Mianyang 621010, PR China

Abstract

Let $R$ be a commutative ring with identity and let $M$ be a $w$-module over $R$. Denote by $\mathscr{F}_M$ the set of all $w$-submodules of $M$ such that $(M/N)_w$ is $w$-cofinitely generated. Then it is shown that $M$ is $w$-Artinian if and only if $\mathscr{F}_M$ is closed under arbitrary intersections, if and only if $\mathscr{F}_M$ satisfies the descending chain condition.


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Supporting Agencies

Changwon National University

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