Zur Fortsetzung von o-Stellen angeordneter Divisionsalgebren. (On extensions of o-places of ordered division algebras)
type: Item
instance of: scholarly article
title: Zur Fortsetzung von o-Stellen angeordneter Divisionsalgebren. (On extensions of o-places of ordered division algebras)
zbMATH Open document ID: 0659.51018
DOI: 10.1007/BF01206477
author: Peter Hartmann
author: Sibylla Priess-Crampe
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: It is well-known that any place of a commutative field F can be extended to a place of any commutative extension field of F. An analogous result for ternary fields is not true in general. The present authors study this question for an ordered (not necessarily associative) division algebra K which contains an ordered division subalgebra F. They show that any order compatible place of F can be extended to an order compatible place of K. Geometrically, this means that any order preserving epimorphism of an ordered projective plane \({\mathcal F}\) of Lenz class at least V can be extended to an order preserving epimorphism of any ordered projective plane of Lenz class at least V which contains \({\mathcal F}\) as a subplane. Recently a similar result for nearfields has been proved by \textit{F. Kalhoff} [Result Math. 15, 66-74 (1989)].
Mathematics Subject Classification ID: 51G05
Mathematics Subject Classification ID: 51A10
Mathematics Subject Classification ID: 17A35
zbMATH DE Number: 4078138
zbMATH Keywords: ordered division algebra
zbMATH Keywords: extension of places
reviewed by: Norbert Knarr
MaRDI profile type: Publication
cites work: Über Homomorphismen projektiver Ebenen
cites work: Valuation theory
cites work: Q3223453
description: scientific article; zbMATH DE number 4078138