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

Main Article Content

Hwankoo Kim
Tae In Kwon
De Chuan Zhou


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.

Article Details

Supporting Agencies

Changwon National University


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