Auslander-Reiten Sequences for "Nice" Torsion Theories of Artinian Algebras

Abstract

Let t be a field and a finite dimensional t-algebra. Auslander-Reiten sequences [AR] play a fundamental rôle in the representation theory of ; in particular, they can be used to construct new indecomposable modules from known ones. For the latter reason I think it worthwile to point out certain torsion theories on the category of -modules, such that the category of -torsionfree modules has Auslander-Reiten sequences; thus giving another construction of indecomposable modules.