Auslander Reiten conjecture and functor Jk2

Abstract.

Recently, Auslander and Reiten initiated the study of k-Gorenstein artin algebra. They conjectured that if an artin algebra $\it\Lambda$ is k-Gorenstein for all k, then it is Gorenstein (see Section 1 for the definitions). In this paper we prove equivalent conditions of the Auslander Reiten conjecture in term of the functor J _k ² and others.