Finite Tor dimension and failure of coherence in absolute integral closures
type: Item
instance of: scholarly article
title: Finite Tor dimension and failure of coherence in absolute integral closures
zbMATH Open document ID: 0908.13006
DOI: 10.1016/S0022-4049(97)00049-2
author: Ian M. Aberbach
author: Melvin Hochster
published in: Journal of Pure and Applied Algebra
publication date: 1999-03-18T00:00:00Z
review text: Let \(R\) be a commutative ring with identity. The authors show that if either \(R\) is a perfect ring of characteristic \(p>0\) or else \(R/pR\) is perfect, then under additional conditions, the radical of a finitely generated ideal has finite Tor dimension. As application, it is proved that \(R^+\) is not coherent when \(R\) is a Noetherian domain of dimension \(\geq 3\), and, under additional restrictions, when \(\dim (R)=2\), where \(R^+\) denotes the integral closure of the domain \(R\) in an algebraic closure of its field of fractions.
reviewed by: Toma Albu
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13A35
zbMATH DE Number: 1097603
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: tight closure
zbMATH Keywords: Frobenius endomorphism
zbMATH Keywords: perfect ring
zbMATH Keywords: radical
zbMATH Keywords: Tor dimension
zbMATH Keywords: integral closure
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1097603