Differential algebra

Locally nilpotent derivation

In mathematics, a derivation of a commutative ring is called a locally nilpotent derivation (LND) if every element of is annihilated by some power of . One motivation for the study of locally nilpotent derivations comes from the fact that some of the counterexamples to Hilbert's 14th problem are obtained as the kernels of a derivation on a polynomial ring. Over a field of characteristic zero, to give a locally nilpotent derivation on the integral domain , finitely generated over the field, is equivalent to giving an action of the additive group to the affine variety . Roughly speaking, an affine variety admitting "plenty" of actions of the additive group is considered similar to an affine space. (Wikipedia).

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