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Incidence Systems associated with Non-Planar Nearfields

Published online by Cambridge University Press:  20 November 2018

Elwyn H. Davis
Elwyn H. Davis*
Affiliation:
Kansas State College of Pittsburg, Pittsburg, Kansas
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In [2] Sandler studied generalizations of projective planes called pseudo planes. These structures gave rise to ternary operations for which addition and multiplication are loop operations. Our aim in this paper is to investigate the pseudo planes for which the operations of addition and multiplication give rise to nearfields. The pseudo planes for which this is true will be called π-systems in this paper, and a list of postulates for such systems is given in § 2. In that section some results on collineations of π-systems are given which are stronger than analogous results for general pseudo planes.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 939 - 952
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. André, J., Projective Ebenen über Fastkorpern, Math. Z. 62 (1955), 137–160.Google Scholar
2. Sandler, R., Pseudo planes and pseudo ternaries, J. Algebra 4 (1966), 300–316.Google Scholar
3. Zemmer, J., Nearfields, planar, and non-planar, Math. Student 81 (1964), 145–150.Google Scholar