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On The Coordinatization Theorem Of J. Von Neumann

Published online by Cambridge University Press:  20 November 2018

K. D. Fryer  and
Israel Halperin
K. D. Fryer
Affiliation:
Royal Military College
Israel Halperin
Affiliation:
Queen's University
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A classical theorem of n-dimensional projective geometry asserts: if Desargues' theorem holds (in particular, if n ≥ 3) then the points of the geometry can be assigned homogeneous coordinates (α1, … , αn+l) with αi not all zero in a suitable division ring (2, p. 104; 3, Theorems 10, 11, ex. 19, p. 204).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 432 - 444
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Fryer, K. D. and Halperin, Israel, Coordinates in Geometry, Trans. Royal Soc. of Canada, Third Series, Section III, 48 (1954), 11–26.Google Scholar
2. Hilbert, D., Grundlagen der Geometrie, seventh edition (Berlin, 1930).Google Scholar
3. Veblen, O. and Young, J. W., Projective Geometry, Vol. I (New York, 1938).Google Scholar
4. von Neumann, J., Continuous Geometry, Vol. I, planographed lecture notes, Institute for Advanced Study (Princeton, 1936).Google Scholar
5. von Neumann, J., Continuous Geometry, Vol. II, planographed lecture notes, Institute for Advanced Study (Princeton, 1936).Google Scholar