# On the depth of tensor products of modules

## TL;DR

This paper investigates the depth of tensor products of modules over Gorenstein local rings, providing formulas under certain homological vanishing conditions, thus advancing understanding in module theory.

## Contribution

It offers new formulas for the depth of tensor products of modules over Gorenstein rings based on Tate and relative homology vanishing assumptions.

## Key findings

- Depth of tensor products can be explicitly determined.
- Results depend on vanishing of specific homology modules.
- Advances understanding of module tensor products over Gorenstein rings.

## Abstract

The depth of tensor product of modules over a Gorenstein local ring is studied. For finitely generated modules M and N over a Gorenstein local ring R, under some assumptions on the vanishing of finite number of Tate and relative homology modules, the depth($M\otimes N$) is determined in terms of the depth(M) and depth(N).