Some results on the kernels of higher derivations on $k[x, y]$ and $k(x, y)$
Colloquium Mathematicum, Tome 122 (2011) no. 2, pp. 185-189
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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
$\overline D$ 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
$ \overline { D}$ is equal to the quotient field of the kernel of $D$.
Keywords:
field polynomial ring variables higher k derivation overline extension prove kernel equal kernel overline equal quotient field kernel
Affiliations des auteurs :
Norihiro Wada 1
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author = {Norihiro Wada},
title = {Some results on the kernels of higher derivations on $k[x, y]$ and $k(x, y)$},
journal = {Colloquium Mathematicum},
pages = {185--189},
publisher = {mathdoc},
volume = {122},
number = {2},
year = {2011},
doi = {10.4064/cm122-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm122-2-3/}
}
TY - JOUR AU - Norihiro Wada TI - Some results on the kernels of higher derivations on $k[x, y]$ and $k(x, y)$ JO - Colloquium Mathematicum PY - 2011 SP - 185 EP - 189 VL - 122 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm122-2-3/ DO - 10.4064/cm122-2-3 LA - en ID - 10_4064_cm122_2_3 ER -
Norihiro Wada. Some results on the kernels of higher derivations on $k[x, y]$ and $k(x, y)$. Colloquium Mathematicum, Tome 122 (2011) no. 2, pp. 185-189. doi: 10.4064/cm122-2-3
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