Birational extensions in dimension two and integrally closed ideals
type: Item
instance of: scholarly article
title: Birational extensions in dimension two and integrally closed ideals
zbMATH Open document ID: 0658.13017
DOI: 10.1016/0021-8693(88)90274-8
author: Craig Huneke
author: Judith D. Sally
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Soient (R,M) un anneau local noethérien de dimension 2 de corps des fractions K et (S,N) un anneau local noethérien normal de dimension 2 tel que \(R\subseteq S\subseteq K\) et \(N\cap R=M\). On suppose, de plus, que R est un anneau régulier maximal contenu dans S et R/M est un corps infini. Les auteurs démontrent des propriétés de l'anneau S. Si la multiplicité \(e(S)=2\), alors MS est un idéal premier. Si S n'est pas régulier, alors S/MS est un anneau de Cohen-Macaulay et MS est un idéal normal. S est un anneau de Gorenstein si et seulement si \(e(S)=2\). Si, de plus, R/M est algébriquemet clos et MS est premier, alors S est un anneau de Gorenstein. S'obtient aussi des résultats sur les idéaux intégralement clos et quelques résultats pour dimension \(>2\).
reviewed by: Nicolae Radu
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 13H99
zbMATH DE Number: 4075249
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: regular local ring
zbMATH Keywords: multiplicity
zbMATH Keywords: Gorensteinness
zbMATH Keywords: integrally closed ideal
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90274-8
OpenAlex ID: W1979261538
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description: scientific article; zbMATH DE number 4075249