Valuations and Dedekind's Prague theorem
type: Item
instance of: scholarly article
title: Valuations and Dedekind's Prague theorem
zbMATH Open document ID: 0983.11061
DOI: 10.1016/S0022-4049(99)00095-X
author: Thierry Coquand
author: Henrik Persson
published in: Journal of Pure and Applied Algebra
publication date: 2002-04-10T00:00:00Z
review text: The paper contains an effective proof of the following theorem of Dedekind: If \(f\) and \(g\) are polynomials in one indeterminate whose cofficients are algebraic numbers, and if all the coefficients of \(fg\) are algebraic integers, then the product of any coefficient of \(f\) with any coefficient of \(g\) is an algebraic integer. The proof is based on properties of the entailment relation of \textit{D. Scott} [Proc. Symp. Pure Math. 25, 411-435 (1974; Zbl 0318.02021)]. The authors also recover a result from Hilbert's Zahlbericht and present other applications of entailment relations.
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 1563008
zbMATH Keywords: Dedekind's Prague theorem
zbMATH Keywords: entailment relations
reviewed by: Doru Ştefănescu
MaRDI profile type: Publication
cites work: Polynomials and radical ideals
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full work available at URL: s0022-4049(99)00095-x
OpenAlex ID: W2056216010
description: scientific article; zbMATH DE number 1563008