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.

Detalles Bibliográficos
Autor: Planas Vilanova, Francesc d'Assís|||0000-0001-6200-1189
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
Descripción
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.