Integral closures of ideals generated by regular sequences
type: Item
instance of: scholarly article
title: Integral closures of ideals generated by regular sequences
zbMATH Open document ID: 0653.13003
DOI: 10.1016/0021-8693(88)90114-7
author: Shiroh Itoh
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: In a Noetherian ring A, let q be an ideal generated by an A-regular sequence \(x_ 1,...,x_ d\). Let R be the Rees ring \(\sum_{n\in Z}q^ nt^ n\quad and\) let \(R'=\sum (q^ n)^*t^ n\quad where\) \((\quad)^*\) denotes integral closure. Theorem: \(q^ n\cap (q^{n+1})^*=q^ nq^*\) for all \(n\geq 1\). This follows from the vanishing of the cohomology modules \(H^ 2_ J(R')_ n\) when \(n\leq 0\), \(J=(t^{-1},x_ 1t,...,x_ rt)R\) and \(2\leq r\leq d.\) Various applications are given. In Hiroshima Math. J. 17, 373-375 (1987; Zbl 0642.13006), the author deduced the theorem for q an ideal of the principal class and A locally quasi-unmixed.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 14B15
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 4065130
zbMATH Keywords: local cohomology module
zbMATH Keywords: regular sequence
zbMATH Keywords: integral closure
reviewed by: C. P. L. Rhodes
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90114-7
OpenAlex ID: W2089272628
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description: scientific article; zbMATH DE number 4065130