Journal of Geometry

, Volume 18, Issue 1, pp 113–121 | Cite as

Desarguessche Axiome in fastaffinen Räumen einer Dimension Grösser als zwei

  • Helga Tecklenburg
Article

Abstract

Nearaffine spaces were introduced by J. ANDRé [1] as a generalization of affine spaces. Desarguesian semi-regular nearaffine spaces can be described as spaces over nearfields (cf. [2]). We show that the Desargues-theorems are valid in every nearaffine space, whose dimension is equal to or larger than three.

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Literaturverzeichnis

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    ANDRÉ, J.: On finite non-commutative affine spaces. In:Combinatorics, ed. by M. HALL jun. and J.H. van LINT, 2nd ed., Mathematical Centre, Amsterdam 1975, 65–113.Google Scholar
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    ANDRé, J.: Affine Geometrien über Fastkörpern. Mitt. Math. Sem. Giessen, Heft114 (1975), 1–99.Google Scholar
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    ANDRé, J.: Introduction to non-commutative affine Geometry. Lectures held at Kuwait University, March 1979.Google Scholar
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    HISCHER, D.: Schließungsaussagen in fastaffinen Räumen. Mitt. Math. Sem. Giessen, Heft131 (1978), 1–95.Google Scholar
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    MISFELD, J., H.TECKLENBURG; Dimension of nearaffine spaces. Proceedings of the Conference of Geometry and Differential Geometry, Haifa 1979. In: Lecture Notes in Mathematics, Vol.792 (1980), 97–109.Google Scholar
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    TECKLENBURG, H.: Algebraische Darstellung fastaffiner Ebenen. Erscheint demnächst.Google Scholar

Copyright information

© Birkhäuser Verlag 1982

Authors and Affiliations

  • Helga Tecklenburg
    • 1
  1. 1.Institut für MathematikUniversität HannoverHannover

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