Nagata criterion for Serre's \((R_n)\) and \((S_n)\)-conditions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0990.14001
author: Ryo Takahashi
publication date: 2002-08-07T00:00:00Z
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 1590695
zbMATH Keywords: regularity
zbMATH Keywords: Serre conditions
zbMATH Keywords: loci of primes
MaRDI profile type: Publication
title: Nagata criterion for Serre's \((R_n)\) and \((S_n)\)-conditions
published in: Mathematical Journal of Okayama University
review text: Let \(A\) be a commutative, noetherian ring. Nagata's criterion gives an axiomatic procedure for proving that some geometric loci of Spec\((A)\) are open. The author shows directly that Nagata's criterion applies to the loci of primes satisfying Serre's \((R_n)\) or \((S_n)\) regularity conditions (for all \(n\geq 0\)), and hence these loci are open in Spec(\(A\)).
reviewed by: Luca Chiantini
description: scientific article