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, Volume 29, Issue 2–4, pp 147–157 | Cite as

Invariante Zwischenkörper endlicher Körpererweiterungen

  • Franz Pauer


Let K⊂M be a finite field extension. An intermediate field L is called “invariant” if there is an affine algebraic K-group acting on M with L as its invariant field. The question, which intermediate fields are invariant, was studied by Bégueri [1] for purely inseparable extensions and by Sweedler [6] for arbitrary extensions, but only for a restricted class of groups. In this paper Bégueri's result is generalized to arbitrary field extensions. Additionally it is shown that one can check whether a given intermediate field is invariant or not by computing the rank of certain matrices. As an application we get a class of invariant intermediate fields.


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  1. [1]
    Bégueri, L.: Schéma d'automorphismes. Application a l'étude d'extensions finies radicielles. Bull. Sc. Math., 2e série, vol. 93, 89–111 (1969)Google Scholar
  2. [2]
    Demazure, M., Gabriel, P.: Groupes algèbriques. Paris: Masson 1970Google Scholar
  3. [3]
    Jacobson, N.: Lectures in Abstract Algebra. Vol. III. Princeton: Van Nostrand 1964Google Scholar
  4. [4]
    Pauer, F.: Spezielle Algebren und transitive Operationen. Math. z. 160, 103–134 (1978)Google Scholar
  5. [5]
    Rasala, R.: Inseparable splitting theory. Trans. Amer. Math. Soc. 162, 411–448 (1971)Google Scholar
  6. [6]
    Sweedler, M.: The Hopf Algebra of an Algebra Applied to Field Theory. J. Algebra 8, 262–276 (1968)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Franz Pauer
    • 1
  1. 1.Institut für MathematikUniversität InnsbruckInnsbruckÖsterreich

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