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

## TL;DR

This paper proves a Bass equality relating the Gorenstein injective dimension of modules finite over a local ring homomorphism to the depth of the ring, extending classical homological results.

## Contribution

It establishes a Bass equality for Gorenstein injective dimension of modules finite over local ring homomorphisms, linking homological and depth invariants.

## Key findings

- Gorenstein injective dimension equals the depth of the ring when finite
- Extends classical Bass equality to Gorenstein homological context
- Provides new insights into homological dimensions over ring homomorphisms

## Abstract

Let $R \to S$ 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 $R$.