Subinjectivity Relative to Cotorsion Pairs

Yusuf Alagöz, Rafail Alizade, Engin Büyükaşık, Juan Ramón García Rozas () and Luis Oyonarte
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Yusuf Alagöz: Department of Mathematics, Hatay Mustafa Kemal University, 31060 Hatay, Turkey
Rafail Alizade: School of Information Technologies and Engineering, Ada University, AZ1008 Baku, Azerbaijan
Engin Büyükaşık: Department of Mathematics, İzmir Institute of Technology, 35430 İzmir, Turkey
Juan Ramón García Rozas: Department of Mathematics, University of Almería, 04120 Almería, Spain
Luis Oyonarte: Department of Mathematics, University of Almería, 04120 Almería, Spain

Mathematics, 2025, vol. 13, issue 12, 1-24

Abstract: In this paper, we define and study the X -subinjectivity domain of a module M where X = ( A , B ) is a complete cotorsion pair, which consists of those modules N such that, for every extension K of N with K / N in A , any homomorphism f : N → M can be extended to a homomorphism g : K → M . 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 X -indigent modules—that is, the modules whose X -subinjectivity domains are as small as possible—for the cotorsion pair X = ( FC , FI ) , where FI is the class of FP-injective modules. Additionally, we determine the rings for which all (simple) right modules are either X -indigent or FP-injective. We further investigate X -indigent Abelian groups in the category of torsion Abelian groups for the well-known example of the flat cotorsion pair X = ( FL , EC ) , where FL is the class of flat modules.

Keywords: cotorsion pairs; X-subinjectivity domains; X-indigent modules; (FP-)injective modules (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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