A counterexample to Hilbert's fourteenth problem in dimension six (Q1972291)

The author constructs a derivation of the polynomial algebra in six indeterminates over a field of characteristic zero, the kernel of which is a subalgebra which cannot be finitely generated. Already the author and D. Daigle have used this example to describe a derivation with the same property for a polynomial algebra in five indeterminates [\textit{D. Daigle} and \textit{G. Freudenburg}, J. Algebra 221, 528-535 (1999; Zbl 0963.13024)]. It is in this paper, however, that details of a rather intricate construction have been carefully organized for ready verification by the reader.