Tight closure and graded integral extensions
type: Item
instance of: scholarly article
title: Tight closure and graded integral extensions
zbMATH Open document ID: 0826.13008
published in: Journal of Algebra
publication date: 1995-11-27T00:00:00Z
review text: For a Noetherian \(\mathbb{N}\)-graded domain \(R\), let \(R^+\) be the integral closure of \(R\) in an algebraic closure of the fraction field of \(R\), and let \(R^{+ gr}\) be the \(\mathbb{N}\)-graded ring generated by homogeneous elements of integral degree in \(R^+\). For an ideal \(I\) of \(R\) generated by a homogeneous system of parameters, the tight closure of \(I\) is equal to \(IR^{+ gr} \cap R\). This is obtained as a consequence of an analogous result for excellent local domains due to the author [Invent. Math. 115, No. 1, 41-60 (1994; Zbl 0820.13007)].
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13B02
zbMATH DE Number: 783936
zbMATH Keywords: integral closure
zbMATH Keywords: integral degree
zbMATH Keywords: tight closure
author: K. E. Smith
reviewed by: C. P. L. Rhodes
MaRDI profile type: Publication
full work available at URL: jabr.1995.1201
OpenAlex ID: W2069248750
DOI: 10.1006/JABR.1995.1201
description: scientific article; zbMATH DE number 783936