Curves and coherent Prüfer rings
type: Item
instance of: scholarly article
title: Curves and coherent Prüfer rings
zbMATH Open document ID: 1203.13020
author: Thierry Coquand
author: Claude Quitté
author: Henri Lombardi
published in: Journal of Symbolic Computation
publication date: 2010-11-19T00:00:00Z
review text: The goal of the paper under review is to show, in constructive mathematics, that if \(k\) is a discrete field (that is, an explicit field with a zero test) and \(f\) an arbitrary polynomial in \(k[x,y]\) then the localization \((k[x,y]/(f))_{f_y}\) is always a coherent Prüfer ring, where \(f_y=\frac{\partial f}{\partial y}\). One important corollary is that \(k[x,y]/(f)\) is a coherent Prüfer ring whenever \(1=(f, f_x,f_y)\). The paper concludes with a {tt magma} program and some examples.
reviewed by: Parviz Sahandi
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 5817629
zbMATH Keywords: semihereditary ring
zbMATH Keywords: pp-ring
zbMATH Keywords: Prüfer ring
zbMATH Keywords: smooth curve
zbMATH Keywords: constructive mathematics
zbMATH Keywords: generalized Hasse derivatives
MaRDI profile type: Publication
full work available at URL: j.jsc.2010.06.016
OpenAlex ID: W2091920640
cites work: Q4950147
cites work: CONSTRUCTIVE KRULL DIMENSION I: INTEGRAL EXTENSIONS
cites work: Algorithmic theory of arithmetic rings, Prüfer rings and Dedekind rings. (Théorie algorithmique des anneaux arithmétiques, des anneaux de Prüfer et des anneaux de Dedekind.)
cites work: A course in constructive algebra
DOI: 10.1016/J.JSC.2010.06.016
description: scientific article; zbMATH DE number 5817629