The Depth Formula for modules over quotients of Gorenstein rings
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912583192150016 |
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| author | An, Tran Nguyen Quy, Pham Hung |
| author_facet | An, Tran Nguyen Quy, Pham Hung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Depth Formula for modules over quotients of Gorenstein rings An, Tran Nguyen Quy, Pham Hung Commutative Algebra 13D45, 13C15, 13H10 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. |
| title | The Depth Formula for modules over quotients of Gorenstein rings |
| topic | Commutative Algebra 13D45, 13C15, 13H10 |
| url | https://arxiv.org/abs/2509.09447 |