  It 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.
