A going-down theorem for real spectra
type: Item
instance of: scholarly article
title: A going-down theorem for real spectra
zbMATH Open document ID: 0688.14020
DOI: 10.1016/0021-8693(89)90130-0
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: The aim of this note is to obtain the following theorem: Let \(\psi\) : \(A\to B\) be a regular homomorphism of noetherian rings, A excellent, and \(\psi^*:\quad Y\to X\) the corresponding map of real spectra. For any prime cones \(\alpha '\to \alpha\) in X and \(\beta\in Y\) with \(\psi^*\beta =\alpha\), there is \(\beta '\in Y\) with \(\beta '\to \beta,\) \(\psi^*\beta '=\alpha ',\) \(ht(\beta ')=ht(\alpha ').\) For the notion of the real spectrum the author refers to \textit{M. Coste} and \textit{M.-F. Roy}, Contemp. Math. 8, 27-59 (1982; Zbl 0485.14007).
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 12D99
zbMATH DE Number: 4127380
zbMATH Keywords: map of real spectra
author: Jesús M. Ruiz
reviewed by: A.F.T.W.Rosenberg
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90130-0
OpenAlex ID: W2087247442
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description: scientific article; zbMATH DE number 4127380