Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-14T22:45:00.126Z Has data issue: false hasContentIssue false
  • English
  • Français

On Ordered Geometries

Published online by Cambridge University Press:  20 November 2018

P. Scherk
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In Theorem 2.20 of his Geometric Algebra, Artin shows that any ordering of a plane geometry is equivalent to a weak ordering of its skew field. Referring to his Theorem 1. 16 that every weakly ordered field with more than two elements is ordered, he deduces his Theorem 2.21 that any ordering of a Desarguian plane with more than four points is (canonically) equivalent to an ordering of its field. We should like to present another proof of this theorem stimulated by Lipman's paper [this Bulletin, vol.4, 3, pp. 265-278]. Our proof seems to bypass Artin's Theorem 1. 16; cf. the postscript.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 1 , January 1963 , pp. 27 - 36
Copyright
Copyright © Canadian Mathematical Society 1963