A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms

Let R→S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R\rightarrow S$$\end{document} be a local ring homomorphism and N a finitely generated S-module. We prove that if the Gorenstein injective dimension of N over R is finite, then it equals the depth of R.