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On Planar Local Nearrings and Bacon Spreads

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Part of the Mathematics and Its Applications book series (MAIA, volume 336)

Abstract

The notion of a planar local nearring is introduced and it is shown, that a planar local nearring N is abelian and gives rise to a certain partial group cover on N × N, called a Bacon spread. Conversely, fixing two normal cover groups {X, Y} with T = X + Y, one can define on a Bacon spread Τ a certain centralizer nearring N Τ(X,Y), called the nucleus, which is a local nearring. Further N Τ(X,Y) is planar and coordinatizes Τ, if it acts transitively on some group of the cover.

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5. References

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    Bacon, P. Y.: An introduction to Klingenberg planes, Volume 3. Published by P. Y. Bacon, 3101 NW 2nd Av., Gainesville, FL 32607 (1979).Google Scholar
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    Kolb, E.: The Schwan/Artin coordinatization for nearfield planes, t. a. in Geo. Ded.Google Scholar
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    Maxson, C. J.: On local near-rings. Math. Z. 106 (1968), 197–205.MathSciNetzbMATHCrossRefGoogle Scholar
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    Wähling, H.: Theorie der Fastkörper. Thales Verlag, Essen (1987).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtGermany

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