2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167988The Nakayama conjecture is one of the most important conjectures in ring theory. The Auslander-Reiten conjecture is closely related to it. The purpose of this note is to show that if the Auslander-Reiten conjecture holds in codimension one for a commutative Gorenstein ring $R$, then it holds for $R$.*** 4 pages, minor changes, to appear in Proc. Amer. Math. SocCommutative AlgebraRings and Algebras13H10, 13D02, 13D07text