Rings whose mininjective modules are injective

ALAGÖZ Y., Benli-Göral S., Büyükaşık E., García Rozas J. R., Oyonarte L.

Communications in Algebra, cilt.53, sa.12, ss.5302-5314, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 12
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/00927872.2025.2509829
  • Dergi Adı: Communications in Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.5302-5314
  • Anahtar Kelimeler: (min) injective modules, Almost injective modules, quasi V-rings, quasi-Frobenius rings, strongly min-coherent rings
  • Hatay Mustafa Kemal Üniversitesi Adresli: Evet

Özet

The main goal of this paper is to characterize rings over which the mininjective modules are injective, so that the classes of mininjective modules and injective modules coincide. We show that these rings are precisely those Noetherian rings for which every min-flat module is projective and we study this characterization in the cases when the ring is Kasch, commutative and when it is quasi-Frobenius. We also treat the case of (Formula presented.) upper triangular matrix rings, proving that their mininjective modules are injective if and only if (Formula presented.). We use the developed machinery to find a new type of examples of indigent modules (those whose subinjectivity domain contains only the injective modules), whose existence is known, so far, only in some rather restricted situations.