• Korean Journal of Mathematics
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• v.28 no.4
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• pp.907-913
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• 2020

Let R be a commutative ring with identity and let M be a w-module over R. Denote by ℱM 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 ℱM is closed under arbitrary intersections, if and only if ℱM satisfies the descending chain condition.