Rings for which every cosingular module is discrete

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Talebi Y., Hamzekolaee A. R. M., Harmanci A., ÜNGÖR B.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.5, pp.1635-1648, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.500759
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1635-1648
  • Hacettepe University Affiliated: Yes

Abstract

In this paper we introduce the concepts of CD-rings and CD-modules. Let R be a ring and M be an R-module. We call R a CD-ring in case every cosingular R-module is discrete, and M a CD-module if every M-cosingular R-module in sigma[M] is discrete. If R is a ring such that the class of cosingular R-modules is closed under factor modules, then it is proved that R is a CD-ring if and only if every cosingular R-module is semisimple. The relations of CD-rings are investigated with V-rings, GV-rings, SC-rings, and rings with all cosingular R-modules projective. If R is a semilocal ring, then it is shown that R is right CD if and only if R is left SC with Soc(R-R) essential in R-R. Also, being a V-ring and being a CD-ring coincide for local rings. Besides of these, we characterize CD-modules with finite hollow dimension.