On (co)pure Baer injective modules

TL;DR

This paper introduces Q-copure Baer injective modules, a generalization of pure Baer injectivity, and explores their properties and characterizations of rings based on these modules.

Contribution

It defines Q-copure Baer injective modules, proves their embedding properties, and characterizes rings like Q-coregular rings through these modules.

Findings

Every module can be embedded as a Q-copure submodule of a Q-copure Baer injective module.

Characterization of Q-coregular rings via properties of Q-copure Baer injective modules.

Extension properties of maps from Q-copure left ideals to modules.

Abstract

For a given class of R-modules Q, a module M is called Q-copure Baer injective if any map from a Q-copure left ideal of R into M can be extended to a map from R into M. Depending on the class Q, this concept is both a dualization and a generalization of pure Baer injectivity. We show that every module can be embedded as Q-copure submodule of a Q-copure Baer injective module. Certain types of rings are characterized using properties of Q-copure Baer injective modules. For example a ring R is Q-coregular if and only if every Q-copure Baer injective R-module is injective.