Abstract
Let $k$ be a field of characteristic $p \geq 0$ and $A = k[x_0, x_1, x_2, \ldots]$ the polynomial ring in countably many variables over $k$. We construct a rational higher $k$-derivation on $A$ whose kernel is not the kernel of any higher $k$-derivation on $A$. This example extends [5, Example 4].
Funding Statement
This work was supported by JSPS KAKENHI Grant Number JP17K05198.
Citation
Hideo Kojima. "Notes on kernels of rational higher derivations in integrally closed domains." Nihonkai Math. J. 29 (2) 69 - 76, 2018.
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