Abstract
The problem of finite generation of the kernel of a derivation of a polynomial ring is a special case of Hilbert's Fourteenth Problem. It is well known that the answer is affirmative if the derivation is locally nilpotent and having a slice. Van den Essen (1995) conjectured that there exists a counterexample for non-locally nilpotent derivations with a slice. In this paper, we solve this conjecture in the affirmative.
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