A new characterization of Auslander algebras.

Let be a finite dimensional Auslander algebra. For a -module , we prove that the projective dimension of is at most one if and only if the projective dimension of its socle soc is at most one. As an application, we give a new characterization of Auslander algebras and prove that a finite dimensional algebra is an Auslander algebra provided its global dimension gl.d and an injective -module is projective if and only if the projective dimension of its socle is at most one. [ABSTRACT FROM AUTHOR]