Mathematics – Commutative Algebra
Scientific paper
2010-05-06
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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