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arXiv · 2509.09447

The Depth Formula for modules over quotients of Gorenstein rings

Tran Nguyen An·Pham Hung Quy
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Abstract

A foundational result by C. Huneke and V. Trivedi provides a formula for the depth of an ideal in terms of height, computed over a finite set of prime ideals, for rings that are homomorphic images of regular rings. Building on a result by the first author for local quotients of Cohen-Macaulay rings, this paper first gives a new proof and derives a similar formula for the finiteness dimension. Our main result then establishes the depth formula for non-local rings that are homomorphic images of a finite-dimensional Gorenstein ring.

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Tran Nguyen An, Pham Hung Quy. 2025-09-11. The Depth Formula for modules over quotients of Gorenstein rings. https://arxiv.org/abs/2509.09447

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