Regular local rings of dimension four and Gorenstein syzygetic prime ideals

Planas Vilanova, Francesc d'Assís

doi:10.1016/j.jalgebra.2022.02.017

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Planas Vilanova, Francesc d'Assís

Document typeArticle

Defense date2022-07-01

PublisherElsevier

Rights accessRestricted access - publisher's policy (embargoed until 2024-07-01)

All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder

Abstract

Let R be a Noetherian local ring. We prove that R is regular of dimension at most 4 if, and only if, every prime ideal, defining a Gorenstein quotient ring, is syzygetic. We deduce a characterization of these rings in terms of the André-Quillen homology.

CitationPlanas-Vilanova, F.A. Regular local rings of dimension four and Gorenstein syzygetic prime ideals. "Journal of Algebra", 1 Juliol 2022, vol. 601, p. 105-114.

URIhttp://hdl.handle.net/2117/365507

DOI10.1016/j.jalgebra.2022.02.017

ISSN1090-266X

Publisher versionhttps://www.sciencedirect.com/science/article/abs/pii/S0021869322000965

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Regular local rings of dimension four and Gorenstein syzygetic prime ideals

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