Max Modules Relative to a Torsion Theory

Abstract

We introduce the concepts of τ -Max modules and left τ -Max rings which are torsiontheoretic analogues of Max modules and left Max rings. A generalization is obtained of an important theorem by Shock and used to characterize τ -Noetherian rings using τ -Max modules. We then characterize left τ -Max rings and obtain a torsion-theoretic version of a result by Hirano. We conclude with results on τ -short modules, introduced as a torsion analogue of a concept recently defined by Bilhan and Smith.