2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67325In studying Nakayama's 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 Ext^i_Lambda(M,M)=0 for all i \geq 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen--Macaulay normal domains containing the rational numbers, and slightly more generally.12 pages, minor changes, this version to appearCommutative AlgebraRings and Algebras13D07; 16G50; 16E30text