arXiv subjects

Mikiya Tanaka

Publications and source records attributed to Mikiya Tanaka.

2 recordsLinked to original sources

arXiv2010

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

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.

math.AG↗

arXiv2010

Locally nilpotent module derivations and the fourteenth problem of Hilbert

Given a locally nilpotent derivation on an affine algebra $B$ over a field $k$ of characteristic zero, we consider a finitely generated $B$-module $M$ which admits a locally nilpotent module derivation $δ_M$ (see Definition 1.1 below). Let $A=\Ker δ$ and $M_0=\Ker δ_M$. We ask if $M_0$ is a finitely generated $A$-module. In general, there exist counterexamples which are closely related to the fourteenth problem of Hilbert. We also look for some sufficient conditions for finite generation.

math.AC↗