Rings for which every cosingular module is projective

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

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.4, pp.973-984, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.15672/hjms.2018.586
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.973-984
  • Keywords: projective module, cosingular module, delta-cosingular module, GV-ring
  • Ankara University Affiliated: Yes

Abstract

Let R be a ring and M be an R-module. In this paper we investigate modules M such that every (simple) cosingular R-module is M-projective. We prove that every simple cosingular module is M-projective if and only if for N <= T <= M, whenever TAN is simple cosingular, then N is a direct summand of T. We show that every simple cosingular right R-module is projective if and only if R is a right GV-ring. It is also shown that for a right perfect ring R, every cosingular right R-module is projective if and only if R is a right GV-ring. In addition, we prove that if every delta-cosingular right R-module is semisimple, then (Z) over bar (M) is a direct summand of M for every right R-module M if and only if (Z) over bar (delta)(M) is a direct summand of M for every right R-module M.