Shen Li

A new characterization of Auslander algebras.

Abstract:

Let A be a finite dimensional Auslander algebra. For an A-module N, we prove that the projective dimension of N is at most one if and only if the projective dimension of its socle is at most one. Then we give a new characterization of Auslander algebras and prove that a finite dimensional algebra is an Auslander algebra provided its global dimension is at most two and an injective module is projective if and only if the projective dimension of its socle is at most one.