Nihonkai Mathematical Journal

Notes on kernels of rational higher derivations in integrally closed domains

Hideo Kojima

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

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1565048775

Mathematical Reviews number (MathSciNet)
MR3989233

Zentralblatt MATH identifier
07097314

Subjects
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]

Keywords
higher derivation rational higher derivation regular field extension

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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