On the rings whose injective right modules are max-projective

ALAGÖZ Y., Büyükaşık E., Yurtsever H. B.

Journal of Algebra and its Applications, cilt.25, sa.7, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 7
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1142/s0219498826500489
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Injective modules, max-projective modules, max-QF rings
  • Hatay Mustafa Kemal Üniversitesi Adresli: Evet

Özet

Recently, right almost-QF (respectively, max-QF) rings that is the rings whose injective right modules are R-projective (respectively, max-projective) were studied by the first two authors. In this paper, our aim is to give some further characterizations of these rings over more general classes of rings, and address several questions about these rings. We obtain characterizations of max-QF rings over several classes of rings including local, semilocal right semihereditary, right non-singular right Noetherian and right nonsingular right finite dimensional rings. We prove that for a ring R being right almost-QF and right max-QF are not left-right symmetric. We also show that right almost-QF and right max-QF rings are not closed under factor rings. This leads us to consider the rings all of whose factor rings are almost-QF and max-QF.