Rings of weak dimension 1 and syzygetic ideals
We prove that rings of weak dimension one are the rings with all (three-generated) ideals syzygetic. This leads to a characterization of these rings in terms of the Andr\'e-Quillen homology.
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1996 |
| 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:2117/865 |
| Acceso en línea: | https://hdl.handle.net/2117/865 |
| Access Level: | acceso abierto |
| Palabra clave: | Commutative rings Algebra, Homological Rings (Algebra) Ideal of linear type syzygetic ideal weak dimension homology of commutative rings Anells commutatius Homologia, Teoria d' Anells (Àlgebra) 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::13F Arithmetic rings and other special rings |
| Sumario: | We prove that rings of weak dimension one are the rings with all (three-generated) ideals syzygetic. This leads to a characterization of these rings in terms of the Andr\'e-Quillen homology. |
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