Hilbert's fourteenth problem and algebraic extensions
type: Item
instance of: scholarly article
title: Hilbert's fourteenth problem and algebraic extensions
zbMATH Open document ID: 1116.12003
author: Shigeru Kuroda
published in: Journal of Algebra
publication date: 2007-04-11T00:00:00Z
review text: Let \(k\) be a field of characteristic \(0,\) \(k[X]=k[X_{1},....,X_{n}]\) the polynomial ring in \(n\) variables over \(k\) and \(k(X)\) the field of fractions of \(k[X].\) In this paper, in response to Hilbert's fourteenth problem, for \(n=3\) and each \(d\geq 3\) constructive examples have been given to show that there exists a subfield \(L\) of \(k(X)\) containing \(k\) such that \([k(X):L]=d\) and \(L\cap k[X]\) is not a finitely generated \(k\)-algebra. Such counter examples are already known for large \(n.\) Some related open problems are also stated.
Mathematics Subject Classification ID: 12F20
zbMATH DE Number: 5141717
zbMATH Keywords: Transcendental extensions Hilbert's 14th problem
Wikidata QID: Q112881503
reviewed by: Sudesh Kaur Khanduja
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.10.008
OpenAlex ID: W2003439337
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DOI: 10.1016/J.JALGEBRA.2006.10.008
description: scientific article; zbMATH DE number 5141717