Subinjectivity Relative to Cotorsion Pairs

ALAGÖZ Y., Alizade R., Büyükaşık E., García Rozas J. R., Oyonarte L.

Mathematics, cilt.13, sa.12, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 12
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/math13122013
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: (FP-)injective modules, cotorsion pairs, X-indigent modules, X-subinjectivity domains
  • Hatay Mustafa Kemal Üniversitesi Adresli: Evet

Özet

In this paper, we define and study the (Formula presented.) -subinjectivity domain of a module M where (Formula presented.) is a complete cotorsion pair, which consists of those modules N such that, for every extension K of N with (Formula presented.) in (Formula presented.), any homomorphism (Formula presented.) can be extended to a homomorphism (Formula presented.). This approach allows us to characterize some classical rings in terms of these domains and generalize some known results. In particular, we classify the rings with (Formula presented.) -indigent modules—that is, the modules whose (Formula presented.) -subinjectivity domains are as small as possible—for the cotorsion pair (Formula presented.), where (Formula presented.) is the class of FP-injective modules. Additionally, we determine the rings for which all (simple) right modules are either (Formula presented.) -indigent or FP-injective. We further investigate (Formula presented.) -indigent Abelian groups in the category of torsion Abelian groups for the well-known example of the flat cotorsion pair (Formula presented.), where (Formula presented.) is the class of flat modules.