On strong isotopy of Dickson semifields and geometric implications
type: Item
instance of: scholarly article
title: On strong isotopy of Dickson semifields and geometric implications
zbMATH Open document ID: 0944.17002
DOI: 10.1007/BF03322095
author: Bianca Spille
author: Irene Pieper-Seier
published in: Results in Mathematics
publication date: 2000-09-24T00:00:00Z
review text: An affine translation plane \({\mathcal P}\) is an incidence group. If \({\mathcal P}\) admits another abelian group acting regularly, then \({\mathcal P}\) can be coordinatized by a commutative semifield, and conversely. Moreover, \({\mathcal P}\) can be viewed as a commutative incidence group with the other group giving the group structure. Isomorphisms of these incidence groups can be characterized in terms of strong isotopisms of the corresponding multiplication variations of the underlying semifield. The authors study strong isotopisms of Dickson semifields. Special attention is payed to those constructed from absolutely algebraic fields and number fields. In particular, an example is given with countably many equivalence classes of strong isotopy.
Mathematics Subject Classification ID: 17A35
Mathematics Subject Classification ID: 51J99
Mathematics Subject Classification ID: 17A36
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 1185383
zbMATH Keywords: commutative division algebra
zbMATH Keywords: Dickson semifield
zbMATH Keywords: strong isotopism
zbMATH Keywords: affine incidence group
reviewed by: Hubert Kiechle
MaRDI profile type: Publication
cites work: Über ebene affine Inzidenzgruppen. (On plane affine incidence groups)
cites work: Q3336276
cites work: Bemerkungen zu einer Klasse kommutativer Inzidenzgruppen. (Remarks on a class of commutative incidence groups)
cites work: Commutative semifields, two dimensional over their middle nuclei
cites work: Q5523725
cites work: Q5510904
description: scientific article; zbMATH DE number 1185383