On the ring of constants for derivations of power series rings in two variables
Tom 87 / 2001
Colloquium Mathematicum 87 (2001), 195-200
MSC: Primary 12H05; Secondary 13F25.
DOI: 10.4064/cm87-2-5
Streszczenie
Let $k[[x,y]]$ be the formal power series ring in two variables over a field $k$ of characteristic zero and let $d$ be a nonzero derivation of $k[[x,y]]$. We prove that if $\mathop{\rm Ker}\nolimits (d)\neq k$ then $\mathop{\rm Ker}\nolimits (d) =\mathop{\rm Ker}\nolimits (\delta)$, where $\delta$ is a jacobian derivation of $k[[x,y]]$. Moreover, $\mathop{\rm Ker}\nolimits (d)$ is of the form $k[[h]]$ for some $h\in k[[x,y]]$.
