A counterexample to Hilbert's fourteenth problem in dimension 5
type: Item
instance of: scholarly article
title: A counterexample to Hilbert's fourteenth problem in dimension 5
zbMATH Open document ID: 0963.13024
author: Daniel Daigle
author: Gene Freudenburg
published in: Journal of Algebra
publication date: 2000-08-03T00:00:00Z
review text: \textit{G. Freudenburg} has obtained a non-finitely generated subalgebra of the polynomial algebra in six indeterminates over a field of characteristic zero as the kernel of a derivation which is triangular with respect to an ordering of the indeterminates [Transform. Groups 5, No. 1, 61-71 (2000)]. In this paper that example is revisited, and a non-finitely generated subalgebra of the polynomial algebra in five indeterminates is obtained by specialization from that example. After a change of variables, the new example is the kernel of the derivation \(a^2{\partial \over\partial x}+ (ax+b){\partial \over\partial y} +y{\partial \over\partial z}\) for indeterminates \(a,b,x,y\), and \(z\). The arguments, based on properties of derivations and gradings of algebras, are clever; and the paper would be self contained but for the one important reference to the cited paper of the second author.
Mathematics Subject Classification ID: 13N15
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1400105
zbMATH Keywords: ordering of the indeterminates
zbMATH Keywords: derivation
reviewed by: H. F. Kreimer
MaRDI profile type: Publication
full work available at URL: jabr.1999.7987
OpenAlex ID: W2021569771
Wikidata QID: Q124810774
cites work: A counterexample to Hilbert's fourteenth problem in dimension six
cites work: On Roberts' counterexample to the fourteenth problem of Hilbert
cites work: An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's fourteenth problem
cites work: Q5829490
DOI: 10.1006/JABR.1999.7987
description: scientific article; zbMATH DE number 1400105