Regular local rings of dimension four and Gorenstein syzygetic prime ideals
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.
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/365507 |
| Acceso en línea: | https://hdl.handle.net/2117/365507 https://dx.doi.org/10.1016/j.jalgebra.2022.02.017 |
| Access Level: | acceso abierto |
| Palabra clave: | Rings (Algebra) Commutative rings Regular local rings Gorenstein rings syzygetic ideals homology of André-Quillen Anells (Àlgebra) Anells commutatius Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Anells i àlgebres |
| Sumario: | 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. |
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