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 Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-5,
author = {Leonid Makar-Limanov and Andrzej Nowicki},
title = {On the ring of constants for derivations of power series rings in two variables},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {195-200},
zbl = {1020.13007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-5}
}
Leonid Makar-Limanov; Andrzej Nowicki. On the ring of constants for derivations of power series rings in two variables. Colloquium Mathematicae, Tome 89 (2001) pp. 195-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-5/