Gorenstein injective dimension and a generalization of Ischebeck Formula

Abstract

Let $(R,\frak m)$ be a commutative Noetherian local ring and let $M$ and $N$ be 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 $\depth_RM+\sup\{i| {0.1cm}\Ext_R^i(M,N)\neq 0\}=\depth R.$