A note on "A generalization of Roberts' counterexample to the fourteenth problem of Hilbert by S. Kuroda"

TL;DR

This paper refines Kuroda's generalization of Roberts' counterexample to Hilbert's fourteenth problem by providing a simpler construction and a more explicit description of the invariant elements involved.

Contribution

It introduces a more straightforward method for constructing invariants in Kuroda's counterexample, enhancing clarity and precision.

Findings

Simplified construction of invariant elements

More explicit form of invariants

Enhanced understanding of counterexample structure

Abstract

In [4], Kuroda generalized Roberts' counterexample \cite{Roberts} to the fourteenth problem of Hilbert. The counterexample is given as the kernel of a locally nilpotent derivation on a polynomial ring. We replace his construction of the invariant elements by a more straightforward construction and give a more precise form of invariant elements.