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## 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 $h\in k[[x,y]]$.

#### Autorzy

• Leonid Makar-LimanovDepartment of Mathematics
and Computer Science
Bar-Ilan University
52900 Ramat-Gan, Israel
and
Department of Mathematics
Wayne State University
Detroit, MI 48202, U.S.A.
e-mail
• Andrzej NowickiFaculty of Mathematics
and Computer Science
N. Copernicus University
87-100 Torun, Poland
e-mail

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