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Order in Affine and Projective Geometry

Published online by Cambridge University Press:  20 November 2018

Joe Lipman
Joe Lipman*
Affiliation:
Summer Research Institute, Canadian Mathematical Congress
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In this note we give a characterisation of ordered skew fields by certain properties of the negative elements.

Properties of negative elements of a skew field K are then interpreted as statements about "betweenness" in any affine geometry over K, or as statements about "separation" in any projective geometry over K.

In this way, our axioms for ordered fields permit of immediate translation into postulates of order for affine or projective geometry (over a field). The postulates so obtained seem simple enough to be of interest, (cf. [4], p. 22)

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 1 , January 1963 , pp. 37 - 43
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Artin, E., Geometric Algebra, Inter science, 1957.Google Scholar
2. Veblen, and Young, , Projective Geometry, Vol. 1, Ginn and Co., 1910.Google Scholar
3. Veblen, and Young, , Vol. 2, 1918.Google Scholar
4. Coxeter, H. S. M., The Real Projective Plane, McGraw-Hill, 1949.Google Scholar