Skip to main content
SpringerLink
Log in

Eine Kennzeichnung der schwach affinen Räume über Skalarensystemen

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Weak affine spaces have been introduced in [6] and [7] by E. SPERNER. They can be algebraically described by quasimodules. in [8] E. SPERNER constructed quasimodules by nearfields. In [9] and [10] he used more general algebraic structures for this construction and in [5] the author described a generalisation of this method. In this note we give a geometric and algebraic characterization of those weak affine spaces which can be constructed in this way.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literatur

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

    Google Scholar 

  2. ARNOLD, H.-J.: Über eine Klasse von Spernerschen Quasimoduln. Abh. Math. Sem. Univ. Hamburg 31, 206–217, (1967).

    Google Scholar 

  3. ARNOLD, H.-J.: Algebraische und geometrische Kennzeichnung der schwach affinen Vektorräume über Fastkörpern. Abh. Math. Sem. Univ. Hamburg 32, 73–88, (1968).

    Google Scholar 

  4. SEIER, W.: Kollineationen von Translationsstrukturen. Journ. of Geometry 1, 183–195, (1971).

    Google Scholar 

  5. SEIER, W.: Schwach affine Räume über Skalarensystemen und ihre Kollineationsgruppen. (erscheint demnächst in Abh. Math. Sem. Univ. Hamburg).

  6. SPERNER, E.: Verallgemeinerte affine Räume und ihre algebraische Darstellung. Algebr. topol. Foundations Geom. Proc. Colloq., Utrecht, August 1959. Published: Oxford-London-New York-Paris 1962, 167–171.

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

    Google Scholar 

  8. SPERNER, E.: On non-desarguesian geometries. Seminari dell'Istituto Nazionale di Alta Matematica, 1962–63, edito Roma 1964.

  9. SPERNER, E.: Weak affine spaces and their algebraic representation. Wiskunde-Seminare, Universiteit van Stellenbosch, 86–124, (1966).

  10. SPERNER, E.: Zur Geometrie der Quasimoduln. Istituto Nazionale di Alta Matematica, Symposia Mathematica, 5, 421–438, (1971).

    Google Scholar 

  11. TIMM, J.: Eine Klasse schwacher binärer Doppelstrukturen. Abh. Math. Sem. Univ. Hamburg 33, 102–118, (1969).

    Google Scholar 

  12. PICKERT, G.: Projektive Ebenen. Berlin-Göttingen-Heidelberg, Springer 1955.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Werner Seier

Authors
  1. Werner Seier
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Seier, W. Eine Kennzeichnung der schwach affinen Räume über Skalarensystemen. Manuscripta Math 8, 39–57 (1973). https://doi.org/10.1007/BF01317576

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01317576

Search

Navigation