Some results on the kernels of higher derivations on $k[x, y]$ and $k(x, y)$

Norihiro Wada

doi:10.4064/cm122-2-3

Geodesic

Parcourir par

Some results on the kernels of higher derivations on $k[x, y]$ and $k(x, y)$

Norihiro Wada ¹

¹ Graduate School of Science and Technology Niigata University Niigata 950-2181, Japan

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

Résumé

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 $D$.

DOI : 10.4064/cm122-2-3

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

¹ Graduate School of Science and Technology Niigata University Niigata 950-2181, Japan

@article{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 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  -

%0 Journal Article
%A Norihiro Wada
%T Some results on the kernels of higher derivations on $k[x, y]$ and $k(x, y)$
%J Colloquium Mathematicum
%D 2011
%P 185-189
%V 122
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm122-2-3/
%R 10.4064/cm122-2-3
%G en
%F 10_4064_cm122_2_3

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. http://geodesic.mathdoc.fr/articles/10.4064/cm122-2-3/

Cité par Sources :