The Depth Formula for modules over quotients of Gorenstein rings
Commutative Algebra
2025-09-12 v1
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.
Cite
@article{arxiv.2509.09447,
title = {The Depth Formula for modules over quotients of Gorenstein rings},
author = {Tran Nguyen An and Pham Hung Quy},
journal= {arXiv preprint arXiv:2509.09447},
year = {2025}
}
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8 pages