Let d be a k-derivation of k[x,y], where k is a field of characteristic zero. Denote by the unique extension of d to k(x,y). We prove that if ker d ≠ k, then ker = (ker d)0, where (ker d)0 is the field of fractions of ker d.
@article{bwmeta1.element.bwnjournal-article-cmv83i2p267bwm,
author = {Janusz Zieli\'nski},
title = {On the algebra of constants of polynomial derivations in two variables},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {267-269},
zbl = {1057.13017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p267bwm}
}
Zieliński, Janusz. On the algebra of constants of polynomial derivations in two variables. Colloquium Mathematicae, Tome 84/85 (2000) pp. 267-269. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p267bwm/
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