On a Conjecture of Auslander and Reiten

In studying Nakayama\u27s 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that ExtiLambda(M,M)=0 for all i \geq 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten\u27s conjecture for excellent Cohen-Macaulay normal domains containing the rational numbers, and slightly more generally