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arXiv · 2302.00035

On Auslander`s depth formula

Shashi Ranjan Sinha·Amit Tripathi
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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.

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Shashi Ranjan Sinha, Amit Tripathi. 2023-01-31. On Auslander`s depth formula. https://arxiv.org/abs/2302.00035

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