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An example of a simple derivation in two variables. (English) Zbl 1223.13015
Summary: Let $$k$$ be a field of characteristic zero. We prove that the derivation $$D=\partial/\partial x+(y^s+px)(\partial/\partial y)$$, where $$s\geq2$$, $$0\neq p\in k$$, of the polynomial ring $$k[x,y]$$ is simple.

##### MSC:
 13N15 Derivations and commutative rings
##### Keywords:
simple derivation; polynomial ring
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