A counterexample to Hilbert's fourteenth problem in dimension 5
\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.
scientific article; zbMATH DE number 1400105