Two remarks on ordering in absolute planes

Detlef Gröger; Kay Sörensen

doi:10.1007/s00022-019-0517-8

Two remarks on ordering in absolute planes

Detlef Gröger, Kay Sörensen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

As well known, the underlying field K of an Euclidean plane E is Euclidean if and only if E fulfills the Circle Axiom. In this paper we consider an apparently weaker form of the Circle Axiom which leads to weaker properties of K. It will be shown that these weaker properties still characterize Euclidean fields. In the second remark we complete the construction of a certain kind of Hilbert plane considered in Pambuccian and Schacht (Beitr Algebra Geom, 2019. https://doi.org/10.1007/s13366-019-00445-y).

Original language	English
Article number	6
Journal	Journal of Geometry
Volume	111
Issue number	1
DOIs	https://doi.org/10.1007/s00022-019-0517-8
State	Published - 1 Apr 2020

Keywords

Circle axiom
Euclidean field
Pythagorean field

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10.1007/s00022-019-0517-8

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Two remarks on ordering in absolute planes

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Keywords

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