2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72150It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. This paper shows that the same is true under the weaker conditions that A is Gorenstein and that M and N have finite complete intersection dimension. The result is also proved if A is Gorenstein and has finite Cohen-Macaulay type. Similar results are given for two types of non-commutative rings: Frobenius algebras and complete semi-local algebras.18 pages. Paper completely rewritten since version 1 contains an error in the proof of Proposition 2.3Rings and Algebras13D07, 13H10, 16E30, 16E65text