CHARACTERIZATION THEOREMS OF S-ARTINIAN MODULES

ÖZEN M., Naji O., TEKİR Ü., Shum K. P.

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, vol.74, no.4, pp.496-505, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 74 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.7546/crabs.2021.04.03
  • Journal Name: COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, zbMATH
  • Page Numbers: pp.496-505
  • Keywords: Artinian rings, finitely cogenerated rings, S-Artinian rings, finitely S-cogenerated rings, S-Artinian modules, finitely S-cogenerated modules
  • Marmara University Affiliated: Yes

Abstract

A module X over a commutative ring A is called S-Artinian, where S is a given multiplicatively closed subset of A, if every descending chain of sub-modules of X is S-stationary. Using this concept, we give many examples, properties and S-versions of several different known results. Also, we characterize S-Artinian in terms of several modules and rings. For instance, X is S-Artinian if and only if every factor module X/Y is a finitely S-cogenerated A-module.