Extending automorphisms and derivations onto Ore-extensions
type: Item
instance of: scholarly article
title: Extending automorphisms and derivations onto Ore-extensions
zbMATH Open document ID: 1355.16022
author: Christian Karpfinger
author: Henning Koehler
author: Heinz Waehling
published in: Results in Mathematics
publication date: 2015-11-06T00:00:00Z
review text: The authors study the extendability of an automorphism \(\sigma\) of a field \(K\) to an automorphism \(\tau\) of the classical right ring of quotients \(Q= K(x;\alpha,\delta)\) of the Ore-extension \(R= K[x;\alpha,\delta]\) and extendability of \(\sigma\)-derivation \(\varepsilon\) of \(K\) to a \(\tau\)-derivation of \(\sigma\). They provide a criterion for extendability of \(\sigma\). Also they characterize all extensions of automorphisms \(\sigma\) from \(K\) to \(Q\). Under some additional assumptions, the authors obtain a characterization of the extensions of \(\sigma\)-derivations \(\varepsilon\).
reviewed by: Jae Keol Park
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16U20
zbMATH DE Number: 6505281
zbMATH Keywords: Ore-extension
zbMATH Keywords: skew polynomial ring
zbMATH Keywords: skew field
zbMATH Keywords: derivation
Wikidata QID: Q62043121
MaRDI profile type: Publication
full work available at URL: s00025-015-0447-1
OpenAlex ID: W1994688676
cites work: Isomorphic ore extensions
cites work: Isomorphic polynomial rings
cites work: Q4848757
cites work: Q3824531
cites work: Automorphisms of Ore extensions.
cites work: Q4011052
cites work: Theory of non-commutative polynomials
cites work: Derivations of skew polynomial rings
cites work: Automorphisms and Derivations of Skew Polynomial Rings
DOI: 10.1007/S00025-015-0447-1
description: scientific article; zbMATH DE number 6505281