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

Hwankoo Kim, Tae In Kwon, De Chuan Zhou

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.

Keywords


w-cofinitely generated, w-Artinian module

Subject classification

13E10, 13D30

Sponsor(s)

Changwon National University

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