Some results on the kernels of higher derivations on and k(x, y)
Volume 122 / 2011
Colloquium Mathematicum 122 (2011), 185-189
MSC: Primary 13N15; Secondary 13A50.
DOI: 10.4064/cm122-2-3
Abstract
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.
