Kernels of derivations in positive characteristic
type: Item
instance of: scholarly article
title: Kernels of derivations in positive characteristic
zbMATH Open document ID: 1057.13016
author: Shun-Ichiro Okuda
published in: Hiroshima Mathematical Journal
publication date: 2004-10-28T00:00:00Z
review text: This paper deals with the kernels of derivations in positive characteristic. Let \(R\) be an integral domain that is finitely generated over a field \(k\). Let \(D:R\rightarrow R\) be a derivation over \(k\). In J. Symb. Comput. 16, 551--555 (1993; Zbl 0809.13002) \textit{A. van den Essen} gives an explicit algorithm to compute the derivation kernel when the characteristic of \(k\) is zero, \(D\) is locally nilpotent and \(\text{Ker\,}D\) is finitely generated. Here the author gives an algorithm to compute the derivation kernel in positive characteristic, inspired by van den Essen's algorithm, but using a truncated version of the exponential of the derivation. A key point in calculating the derivation kernel is to consider the derivation kernel as a \(k[R^p]\)-module. The algorithm can be implemented by the Singular software programme. The theoretical results are interpreted with the help of several interesting examples.
reviewed by: Vittoria Bonanzinga
Mathematics Subject Classification ID: 13N15
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 13P99
zbMATH DE Number: 2111505
zbMATH Keywords: derivations
zbMATH Keywords: positive characteristic
zbMATH Keywords: integral domain
zbMATH Keywords: Singular
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1150998069
OpenAlex ID: W1527826030
Wikidata QID: Q128872249
DOI: 10.32917/HMJ/1150998069
description: scientific article; zbMATH DE number 2111505