Valuations and the Ritt problem
type: Item
instance of: scholarly article
title: Valuations and the Ritt problem
zbMATH Open document ID: 0593.12012
DOI: 10.1016/0021-8693(86)90093-1
author: Richard M. Cohn
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: The author generalizes his previous result [see Am. J. Math. 108, 505-523 (1986)] concerned with the Ritt problem. He proves by means of methods of valuation theory the following result: Main theorem. Let F be an ordinary differential field of characteristic 0. Let \(\alpha\) be differentially algebraic over F and specializing differentially over F to \(\beta\) with tr deg F\(<\alpha >/F-tr \deg F<\beta >/F\geq 2\). Then there exists \(\alpha^*\) satisfying (1) \(\alpha\) specializes differentially over F to \(\alpha^*;\) (2) there is a rank one valuation \(\mu\) of \(F<\alpha^*>/F\) which is also a differential valuation and which is such that the associated place maps \(\alpha^*\) to \(\beta\), and \(\mu\) is of rational rank less than tr deg F\(<\alpha >/F-tr \deg F<\beta >/F\).
Mathematics Subject Classification ID: 12H05
zbMATH DE Number: 3952900
zbMATH Keywords: Ritt problem
zbMATH Keywords: differential field
zbMATH Keywords: differential valuation
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90093-1
OpenAlex ID: W1980591006
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description: scientific article; zbMATH DE number 3952900