Symmetry in the vanishing of Ext over Gorenstein rings

Abstract

We investigate symmetry in the vanishing of Ext for finitely generated modules over local Gorenstein rings. In particular, we define a class of local Gorenstein rings, which we call AB rings, and show that for finitely generated modules M and N over an AB ring R, ExtRi(M, N) = 0 for all i ≫ 0 if and only if ExtRi (N, M) = 0 for all i ≫ 0.