Let k be a field and k[x,y] the polynomial ring in two variables over k. Let D be a higher k-derivation on k[x,y] and D̅ the extension of D on k(x,y). We prove that if the kernel of D is not equal to k, then the kernel of D̅ is equal to the quotient field of the kernel of D.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-2-3,
author = {Norihiro Wada},
title = {Some results on the kernels of higher derivations on k[x,y] and k(x,y)},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {185-189},
zbl = {1213.13039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-2-3}
}
Norihiro Wada. Some results on the kernels of higher derivations on k[x,y] and k(x,y). Colloquium Mathematicae, Tome 122 (2011) pp. 185-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-2-3/