A NOTE ON SYMMETRY IN THE VANISHING OF EXT

In [2] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, Ext(R)(i) (M, N) = 0 for all i >> 0 implies Ext(R)(i) (N, M) = 0 for all i >> 0. In this note we give some generalizations of this result. Indeed we prove the above-mentioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3) M is complete and N is finitely generated.