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, cilt.49, sa.5, ss.1635-1648, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.500759
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1635-1648
  • Anahtar Kelimeler: CD-module, CD-ring, cosingular module, discrete module, V-ring, semilocal module, finite hollow dimension, TORSION
  • Ankara Üniversitesi Adresli: Evet

Özet

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.