Locally nilpotent module derivations and the fourteenth problem of Hilbert

Details Locally nilpotent module derivations and the fourteenth problem of Hilbert Locally nilpotent module derivations and the fourteenth problem of Hilbert

2010-05-06

arxiv.org/abs/1005.0887v1

Mathematics

Commutative Algebra

17 pages

Scientific paper

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 $\delta_M$ (see Definition 1.1 below). Let $A=\Ker \delta$ and $M_0=\Ker \delta_M$. 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.

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