On J-torsionless modules

TL;DR

This paper introduces the concept of J-torsionless modules, generalizes reject modules, characterizes regularity via J-torsionless modules, and explores conditions for cyclic modules and self-injective rings.

Contribution

It presents the novel concepts of JReject and J-torsionless modules, providing new characterizations and conditions in module theory.

Findings

Characterization of regularity using J-torsionless modules

Necessary and sufficient conditions for cyclic modules to be J-torsionless

Description of self-injective rings where all modules are J-torsionless

Abstract

In this paper, we introduce the concept of JReject of a class of modules as a generalization of the notion of reject of a class of modules. We also introduce the notion of J-torsionless modules and give a characterization of regularity on the basis of the J-torsionless condition. A necessary and sufficient condition on $R$ is also given for every cyclic module over $R$ to be J-torsionless. Finally, we give a description of self-injective rings over which every module is J-torsionless.