Nihonkai Mathematical Journal

Notes on kernels of rational higher derivations in integrally closed domains

Hideo Kojima

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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].


This work was supported by JSPS KAKENHI Grant Number JP17K05198.

Article information

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

Received: 24 July 2018
Revised: 4 October 2018
First available in Project Euclid: 5 August 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]
Secondary: 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]

higher derivation rational higher derivation regular field extension


Kojima, Hideo. Notes on kernels of rational higher derivations in integrally closed domains. Nihonkai Math. J. 29 (2018), no. 2, 69--76.

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