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Noetherian rings of low global dimension and syzygetic prime ideals
| dc.contributor.author | Planas Vilanova, Francesc d'Assís |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| dc.date.accessioned | 2023-05-26T06:50:52Z |
| dc.date.available | 2023-05-26T06:50:52Z |
| dc.date.issued | 2021-02-01 |
| dc.identifier.citation | Planas-Vilanova, F.A. Noetherian rings of low global dimension and syzygetic prime ideals. "Journal of pure and applied algebra", 1 Febrer 2021, vol. 225, núm. 2, article 106494. |
| dc.identifier.issn | 0022-4049 |
| dc.identifier.uri | http://hdl.handle.net/2117/387898 |
| dc.description.abstract | Let R be a Noetherian ring. We prove that R has global dimension at most two if, and only if, every prime ideal of R is of linear type. Similarly, we show that R has global dimension at most three if, and only if, every prime ideal of R is syzygetic. As a consequence, we derive a characterization of these rings using the André-Quillen homology. |
| dc.description.sponsorship | This work is partially supported by the Catalan grant 2014 SGR-634. |
| dc.format.extent | 8 p. |
| dc.language.iso | eng |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
| dc.subject.other | Global dimension |
| dc.subject.other | Noetherian regular rings |
| dc.subject.other | Ideal of linear type |
| dc.subject.other | Syzygetic ideal |
| dc.title | Noetherian rings of low global dimension and syzygetic prime ideals |
| dc.type | Article |
| dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
| dc.identifier.doi | 10.1016/j.jpaa.2020.106494 |
| dc.description.peerreviewed | Peer Reviewed |
| dc.subject.ams | Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory |
| dc.subject.ams | Classificació AMS::13 Commutative rings and algebras::13D Homological methods |
| dc.subject.ams | Classificació AMS::13 Commutative rings and algebras::13H Local rings and semilocal rings |
| dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S002240492030195X |
| dc.rights.access | Open Access |
| local.identifier.drac | 29435130 |
| dc.description.version | Postprint (author's final draft) |
| dc.relation.projectid | info:eu-repo/grantAgreement/AGAUR/2014-SGR-634 (Geometria de varietats i aplicacions) |
| local.citation.author | Planas-Vilanova, F. A. |
| local.citation.publicationName | Journal of pure and applied algebra |
| local.citation.volume | 225 |
| local.citation.number | 2, article 106494 |
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