Integral closedness of complete-intersection ideals
type: Item
instance of: scholarly article
title: Integral closedness of complete-intersection ideals
zbMATH Open document ID: 0629.13004
DOI: 10.1016/0021-8693(87)90128-1
author: Shiro Goto
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: This paper studies the problem when a complete intersection ideal I of a noetherian ring A is integrally closed. Main result: The following conditions are equivalent: \((i)\quad \bar I=I;\) \((ii)\quad \overline{I^ n}=I^ n\) for all \(n\geq 1\); \((iii)\quad For\) each \(p\in Ass(A/I)\), the local ring \(A_ p\) is regular and \(\ell ((IA_ p+p^ 2A_ p)/p^ 2A_ p)\geq r-1\), where \(ht(I)=r\). When this is the case, I is unmixed and it is generated by a regular sequence. The second condition is significant because it is equivalent to the normality of the Rees algebra of I, whereas the third condition gives the precise structure of integrally closed complete intersection ideals. The proof is based on the beautiful theory of full ideals recently developed by D. Rees and J. Watanabe\&(see \textit{J. Watanabe}, Nagoya Math. J. 106, 101-111 (1987; Zbl 0623.13012)].
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13H05
zbMATH DE Number: 4023434
zbMATH Keywords: integral closure
zbMATH Keywords: parameter ideal
zbMATH Keywords: complete intersection ideal
zbMATH Keywords: normality of the Rees algebra
zbMATH Keywords: full ideals
reviewed by: Trung Ngo Viet
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90128-1
OpenAlex ID: W2044139740
cites work: Graded algebras of powers of ideals generated by A-sequences
cites work: Ideals of the principal class, R-sequences and a certain monoidal transformation
cites work: A criterion for complete intersections to be self-radical
cites work: Q5611879
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cites work: m-full ideals
description: scientific article; zbMATH DE number 4023434