## Nihonkai Mathematical Journal

### Notes on kernels of rational higher derivations in integrally closed domains

Hideo Kojima

#### 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].

#### Note

This work was supported by JSPS KAKENHI Grant Number JP17K05198.

#### Article information

Source
Nihonkai Math. J., Volume 29, Number 2 (2018), 69-76.

Dates
Revised: 4 October 2018
First available in Project Euclid: 5 August 2019

https://projecteuclid.org/euclid.nihmj/1565048775

Mathematical Reviews number (MathSciNet)
MR3989233

Zentralblatt MATH identifier
07097314

#### Citation

Kojima, Hideo. Notes on kernels of rational higher derivations in integrally closed domains. Nihonkai Math. J. 29 (2018), no. 2, 69--76. https://projecteuclid.org/euclid.nihmj/1565048775

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