Summary
A geometric space over a geometric sfield of dimension three induces a protective plane. A relation between the order of the projective plane and that of the geometric sfield is obtained. For a particular order of the sfield, the induced projective plane is shown to be desarguesian.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BAER, R.: “Linear Algebra and Projective Geometry”, Academic Press, 1952.
BHATTARAI, H.N.: An Orbit Space Representation of a Geometry, J. Algebra, Vol. 84, No. 1 (1983), 142–150.
---- On Geometric Nearfields, Nep. Math. Sc. Rep., Vol. 5, No. 2 (1980).
---- On Certain sets in Pasch Geometric Modules of dimension three, Nep. Math. Sc. Rep., Vol. 6, No. 1–2 (1981).
HARRISON, D.K.: Double Cosets and Orbit Spaces, Pac. J. Math. 80(2), (1979).
HUGHES, D. and PIPER, F.: “Projective Planes”, Springer-Verlag, New York, 1973.
ZARISKI, O. and SAMUEL, P.: “Commutative Algebra”, Vol. 1, Princeton N.J.: D. Von Nonstrand, 1958.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bhattarai, H.N. Pasch geometric spaces inducing finite projective planes. J Geom 34, 6–13 (1989). https://doi.org/10.1007/BF01224228
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01224228