Journal of Geometry

, Volume 12, Issue 2, pp 99–103 | Cite as

Bemerkung zu Einem Satz von Baer

  • Günter Heimbeck
Article
  • 23 Downloads

Abstract

Let α be an involutorial antiautomorphism of the division ring K with char K ≠ 2 and E := {r ∈ K | rrα = 1}. Refining a result of R. Baer we prove: (card E−1)2 < card K ⇒ α=id. This is done by computing card E and the cardinal numbers of the sets consisting of the α-symmetric respectively the α-skew-symmetric elements.

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Literatur

  1. [1]
    Baer, R.: Linear Algebra and Projective Geometry. New York, Academic Press 1952.Google Scholar
  2. [2]
    Dieudonné, J.: La géométrie des groupes classiques. 2. Auflage. Berlin-Göttingen-Heidelberg, Springer-Verlag 1963.Google Scholar

Copyright information

© Birkhäuser Verlag 1979

Authors and Affiliations

  • Günter Heimbeck
    • 1
  1. 1.Mathematisches Institut Am HublandWürzburg

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