Derivativations of a ring $R$ are additive $f: R \rightarrow R $ functions for which $ f (rs) = rf(s) + f(r) s$. An element $ r \in R $ is a constant of $ f $ if $ f (r) = 0 $. It is clear that they form a subring. We study the derivativations of $n$-variable polynomal algebras over a field. We are interested in which properties of the derivation are reflected by the properties of the algebra of constants.

For a BSc thesis we expect a survey of the important results in a simple aspect of the problem.

For a MSc thesis we expect a fuller survey and a discussion of underlying interconnections.

For a TDK submission we expect the solution of a special case.

For a PhD thesis we expect the solution of several cases or a radically new reinterpretation of a broad area.