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Regular local rings of dimension four and Gorenstein syzygetic prime ideals

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2022Embargo end date: 01 Jan 2021 Spain English Publisher:Elsevier BVJournal:Journal of Algebra, volume 601, pages 105-114 (issn: 0021-8693, Copyright policy )
Authors: Planas Vilanova, Francesc d'Assís;

doi: 10.1016/j.jalgebra.2022.02.017 , 10.48550/arxiv.2105.09161

arXiv: 2105.09161

handle: 2117/365507

Regular local rings of dimension four and Gorenstein syzygetic prime ideals

Abstract

Let $R$ be a Noetherian local ring. We prove that $R$ is regular of dimension at most four 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.

To appear in Journal of Algebra

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Spain
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Keywords

:Matemàtiques i estadística::Àlgebra::Anells i àlgebres [Àrees temàtiques de la UPC], 13A30, 13D02, 13D03, 13H05, 13H10, Rings (Algebra), syzygetic ideals, homology of André-Quillen, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Commutative rings, regular local rings, Anells commutatius, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.), Anells (Àlgebra), Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Gorenstein rings, FOS: Mathematics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Anells i àlgebres, Regular local rings

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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