Compact disconnected Moufang planes are desarguesian
type: Item
instance of: scholarly article
title: Compact disconnected Moufang planes are desarguesian
zbMATH Open document ID: 0624.51009
DOI: 10.1007/BF01200475
author: Theo Grundhöfer
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: The author proves the claim of the title as a corollary of the following Theorem: Every non-discrete locally compact disconnected alternative field A is associative. His first proof relies on the fact that Cayley algebras over local fields do not exist. The author gives a second interesting proof: Extending results of \textit{A. Weil} [Basic Number Theory (1967; Zbl 0176.336)] to alternative fields he uses the modular function on A to construct a 2- element-set generating A. Variants of the second proof are given, one of them using the associativity of locally finite complete alternative fields, proven by \textit{H. van Maldeghem} [J. Geom. 30, 42-48 (1987)].
reviewed by: Horst Szambien
Mathematics Subject Classification ID: 51H05
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 12J20
Mathematics Subject Classification ID: 12K99
zbMATH DE Number: 4013426
zbMATH Keywords: compact disconnected Moufang plane
zbMATH Keywords: modular function of an alternative field
zbMATH Keywords: locally compact disconnected alternative field
MaRDI profile type: Publication
cites work: Charakterisierungen endlicher Desarguesscher uniformer Hjelmslev-Ebenen
cites work: Moufang-Hjelmslev-Ebenen
cites work: Q3972230
cites work: Q3205756
cites work: Q3882586
cites work: Q5675788
cites work: Zur Struktur von Alternativkörpern
cites work: Composition algebras over a field with a discrete valuation
cites work: Topological projective planes
cites work: Topological planes
cites work: Q3228687
cites work: On locally finite alternative division rings with valuation
cites work: Locally Compact Vector Spaces and Algebras over Discrete Fields
cites work: Q5566639
cites work: Q5763684
Recommended article: Compact disconnected planes, inverse limits and homomorphisms
Recommended article: The classification of compact punctually cohesive Desarguesian projective Klingenberg planes
Recommended article: A geometric construction of Moufang planes
Recommended article: Simply connected compact subsets of the plane
Recommended article: Q4335488
Recommended article: Topological properties of locally compact connected Minkowski planes and their derived affine planes
Recommended article: Constructive Coordinatization of Desarguesian Planes
Recommended article: Q4523984
Recommended article: Q3330036
Recommended article: Disjoint embeddings of compacta
description: scientific article; zbMATH DE number 4013426