On R-Coneat Injective Modules and Generalizations
Abstract
Both the classes of $R$-coneat injective modules and its superclass, pure Baer injective modules, are shown to be preenveloping. The former class is contained in another one, namely, self coneat injectives, i.e. modules $M$ into which every homomorphism, whose kernel contains the annihilator of an element in $M$ and whose domain is a coneat left ideal of $R$, can be extended to a homomorphism $R \rightarrow M$. Characterizations of certain types of rings are given using properties of the above modules. For instance, a commutative ring $R$ is von Neumann regular precisely when all self coneat injective $R$-modules are quasi injective.
Fields of Study & Subjects
Rings
Modules
and Algebras
Publication details
- Journal / source
- Missouri Journal of Mathematical Sciences
- Volume
- 38
- Issue
- 1
- Publication date
- 1 May 2026
- Language
- EN