Module Categories with Infinite Radical Cube Zero Original Research Article

LetAbe an artin algebra and let mod Adenote the category of finitely generated rightA-modules. We denote by rad(mod A) the ideal in mod Agenerated by all non-invertible morphisms between indecomposable modules in mod A. The infinite radical rad∞(mod A) of mod Ais the intersection of all powers radi(mod A),i≥1, of rad(mod A). It is known thatAis representation-finite if and only if (rad∞(mod A))2=0. In this paper we study the representation-infinite algebrasAsuch that (rad∞(mod A))3=0. Examples of such algebras include all representation-infinite tilted algebras of Euclidean type.