The plus closure in mixed characteristic
type: Item
instance of: scholarly article
title: The plus closure in mixed characteristic
zbMATH Open document ID: 0902.13006
author: Raymond C. Heitmann
published in: Journal of Algebra
publication date: 1998-12-06T00:00:00Z
review text: Let \(I\) be an arbitrary ideal in an integrally closed domain \(R\). The plus closure of \(I\) is defined to be the ideal \(I^+ = IR^+\cap R\), where \(R^+\) denotes the integral closure of \(R\) in an algebraic closure of its quotient field. \textit{M. Hochster} and \textit{C. Huneke} [Adv. Math. 113, No. 1, 45-117 (1995; Zbl 0834.13013)] have used this notion to prove a generalized Briançon-Skoda theorem which says that if \(R\) is a noetherian ring of characteristic \(p\) and if \(I\) is generated by \(n\) elements, then \(\overline{I^{m+n}}\subseteq (I^{m+1})^+\) for any integer \(m\geq 0\), where \(\overline{J}\) denotes the integral closure of the ideal \(J\). The aim of this paper is to develop a mixed characteristic analogue of this theorem. If \(p \in \sqrt{I}\), the author obtains the desired result in a number of cases which contains the equicharacteristic case as a corollary.
reviewed by: Trung Ngo Viet
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 1051583
zbMATH Keywords: integral closure
zbMATH Keywords: plus closure
zbMATH Keywords: mixed characteristic
zbMATH Keywords: Briançon-Skoda theorem
MaRDI profile type: Publication
full work available at URL: jabr.1997.7023
OpenAlex ID: W2094153426
cites work: Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
cites work: Infinite integral extensions and big Cohen-Macaulay algebras
cites work: Applications of the existence of big Cohen-Macaulay algebras
cites work: Locally quasi-unmixed Noetherian rings and ideals of the principal class
cites work: Q4293985
DOI: 10.1006/JABR.1997.7023
description: scientific article; zbMATH DE number 1051583