On the existence of proper locally maximal torsion classes for finite dimensional algebras

A brick version of a theorem of Auslander

We prove that a finite dimensional algebra is finite if and only if all the bricks over are finitely generated.This isobtained as a consequence of the existence of proper locally maximal torsionclasses for infinite algebras.We prove that a finite dimensional algebra is finiteif and only if all the bricks over are finitely generated.This isobtained as a consequence of the existence of proper locally maximal torsionclasses for infinite algebras.We prove that a finite dimensional algebra is finiteif and only if all the bricks over are finitely generated.This isobtained as a consequence of the existence of proper locally maximal torsionclasses for infinite algebras.We prove that a finite dimensional algebra is finiteif and only if all the bricks over are finitely generated.This isobtained as a consequence of the existence of proper locally maximal torsionclasses for infinite algebras.