Work

Subinjectivity Relative to Cotorsion Pairs

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13122013

Authors: Yusuf Alagöz, Rafail Alizade, Engin Büyükaşık, Juan Ramón García Rozas, Luis Oyonarte

Institutions: Mustafa Kemal University, ADA University, Izmir Institute of Technology, University of Almería

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4411457319

FWCI:

Cites: 25

Cited by:

Related to: 10