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ISomorphismen verallgemeinerter Parallelstrukturen

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Abstract

Incidencestructures with an equivalence relation on the set of blocks or lines, satisfying the euclidean axiom of parallelism, are called generalised parallel structures, if on each line are at least two points and if through two different points passes at most one line. In this paper we give a coordinatization for a class of generalised parallel structures. Isomorphisms of desarguesian affine spaces induce in a well known manner regular semilinear mappings of the corresponding vector spaces. We prove an analogous theorem for generalised parallel structures and the corresponding algebraic structures.

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Literatur

  1. ANDRÉ,J.: Über nicht-desarguessche Ebenen mit transitiver Translationsgruppe. Math. Zeitschr. 60, 156–186 (1954).

    Google Scholar 

  2. ANDRÉ,J.: Über Parallelstrukturen I, II. Math. Zeitschr. 76, 85–102,155–163 (1961).

    Google Scholar 

  3. ANDRÉ,J.: Über verallgemeinerte Translationsstrukturen und ihre Homomorphismen. Arch. Math. XXIII, 198–205 (1972).

    Google Scholar 

  4. ARNOLD,H.-J.: A way to the geometry of rings. Jour. of Geomety 1.2, 155–167 (1971).

    Google Scholar 

  5. DEMBOWSKI,P.: Finite geometries. Berlin-Heidelberg-New York 1968.

  6. SEIER,W.: Kollineationen von Translationsstrukturen. Jour. of Geometry 1.2, 183–195 (1971).

    Google Scholar 

  7. SEIER,W.: Schwach affine Räume über Skalarensystemen und ihre Kollineationsgruppen. Erscheint demnächst in Abh. Hamburg.

  8. SPERNER,E.: Verallgemeinerte affine Räume und ihre algebraische Darstellung. Algebraical and Topological Foundations of Geometry. Proc. of a Coll. in Utrecht, Aug. 1959. Oxford, London, New York, Paris 1962, 167–171.

  9. SPERNER,E.: Affine Räume mit schwacher Inzidenz und zugehörige algebraische Strukturen. Jour. reine u. angew. Math. 204, 205–215 (1960).

    Google Scholar 

  10. SPERNER,E.: Zur Geometrie der Quasimoduln. Istituto Nazionale di Alta Matematica, Symposia Mathematica Volume V (1970).

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Authors and Affiliations

  1. Mathematisches Seminar der Universität, Rothenbaumchaussee 67/69, 2 Hamburg 13

    Werner Seier

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  1. Werner Seier
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Seier, W. ISomorphismen verallgemeinerter Parallelstrukturen. J Geom 3, 165–178 (1973). https://doi.org/10.1007/BF01950056

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  • DOI: https://doi.org/10.1007/BF01950056

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