Gorenstein injective modules and a generalization of ischebeck formula

摘要

Let (R,$rak{m}$) be a commutative Noetherian local ring and let M and N be nonzero finitely generated R-modules of finite injective dimension and finite Gorenstein injective dimension, respectively. In this paper, we prove a generalization of Ischebeck formula, that is ${m depth}-RM+sup{i, |, {m Ext}-R^i(M, N)eq 0} = {m depth}, R$.