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, cilt.48, sa.4, ss.973-984, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.15672/hjms.2018.586
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.973-984
  • Anahtar Kelimeler: projective module, cosingular module, delta-cosingular module, GV-ring
  • Ankara Üniversitesi Adresli: Evet

Özet

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.