Noetherian rings of low global dimension and syzygetic prime ideals
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...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| 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:2117/387898 |
| Acceso en línea: | https://hdl.handle.net/2117/387898 https://dx.doi.org/10.1016/j.jpaa.2020.106494 |
| Access Level: | acceso abierto |
| Palabra clave: | Global dimension Noetherian regular rings Ideal of linear type Syzygetic ideal Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory Classificació AMS::13 Commutative rings and algebras::13D Homological methods Classificació AMS::13 Commutative rings and algebras::13H Local rings and semilocal rings Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | 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. |
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