Geodesic
On the ring of constants for derivations of power series rings in two variables
Leonid Makar-Limanov 1   ; Andrzej Nowicki 2
1 Department 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.
2 Faculty of Mathematics and Computer Science N. Copernicus University 87-100 Torun, Poland
Colloquium Mathematicum, Tome 87 (2001) no. 2, pp. 195-200 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $h\in k[[x,y]]$.
DOI : 10.4064/cm87-2-5
Keywords: formal power series ring variables field characteristic zero nonzero derivation prove mathop ker nolimits neq mathop ker nolimits mathop ker nolimits delta where delta jacobian derivation moreover mathop ker nolimits form

Leonid Makar-Limanov  1   ; Andrzej Nowicki  2

1 Department 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.
2 Faculty of Mathematics and Computer Science N. Copernicus University 87-100 Torun, Poland 
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Leonid Makar-Limanov; Andrzej Nowicki. On the ring of constants
for derivations of power series rings
in two variables. Colloquium Mathematicum, Tome 87 (2001) no. 2, pp. 195-200. doi: 10.4064/cm87-2-5

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