On Auslander`s depth formula
Commutative Algebra
2023-02-02 v1
Abstract
We show that if Auslander`s depth formula holds for non-zero Tor-independent modules over Cohen-Macaulay local rings of dimension 1, then it holds for such modules over any Cohen-Macaulay local ring. More generally, we show that the depth formula for non-zero Tor-independent modules which have finite Cohen-Macaulay dimension over depth 1 local rings implies the depth formula for such modules over any positive depth local ring.
Cite
@article{arxiv.2302.00035,
title = {On Auslander`s depth formula},
author = {Shashi Ranjan Sinha and Amit Tripathi},
journal= {arXiv preprint arXiv:2302.00035},
year = {2023}
}
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