Integral closure and generic elements
type: Item
instance of: scholarly article
title: Integral closure and generic elements
zbMATH Open document ID: 1213.13020
author: Catalin Ciuperca
published in: Journal of Algebra
publication date: 2011-05-16T00:00:00Z
review text: Let \((R,m)\) be a formally equidimensional local ring with \(depth\;R\geq 2\), \(I=(a_1,\dots,a_n)\) an \(m\)-primary ideal of \(R\) and \(T=R[x_1,\dots,x_n]/(\Sigma_{i=1}^n a_ix_i)\). Then the integral closure of \(IT\) in \(T\) is generated by the integral closure of \(I\) in \(R\). Now let \((A,m)\) be a regular local ring, \(I\subset A\) an ideal such that the embedding dimension of \(A/I\) is at most two and \(\bar I\) the integral closure of \(I\) in \(A\). Then \(I^{n-1}{\bar I}\) is the integral closure of \(I^n\) for all \(n\geq 1\).
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 13A30
zbMATH DE Number: 5888484
zbMATH Keywords: integral closure of ideals
zbMATH Keywords: formally equidimensional rings
zbMATH Keywords: almost complete intersection ideals
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.07.025
OpenAlex ID: W2164361431
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DOI: 10.1016/J.JALGEBRA.2010.07.025
description: scientific article; zbMATH DE number 5888484