Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A CHARACTERIZATION OF w-ARTINIAN MODULES

  • Kwon, Tae In (Department of Mathematics Changwon National University) ;
  • Kim, Hwankoo (Division of Computer and Information Engineering Hoseo University) ;
  • Zhou, De Chuan (School of Science Southwest University of Science and Technology)
  • Received : 2020.10.04
  • Accepted : 2020.12.07
  • Published : 2020.12.30
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Abstract

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.

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Acknowledgement

This research was supported by Changwon National University in 2019-2020.

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