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Arfs Theorem in Dimension ℵ0

  • Herbert Gross
Part of the Progress in Mathematics book series (PM, volume 1)

Abstract

In the whole chapter k is a field of characteristic 2 and ξ → ξ * an antiautomorphism of the field whose square is inner, ξ * * = ξ-1 ξ ε and furthermore, ε ε * = 1 for some ε ∈ K . Let as usual S := { ξ ∈ k | ξ = ε ξ * } and T : { ξ + ε ξ * | ξ ∈ k} be the additive subgroups in k of symmetric elements and traces respectively. The factor group S/T is a k-left vector space under the composition λ ( σ + T ) = λ σ λ * + T ( σ ∈ S, λ ∈k).

Keywords

Division Algebra Subspace Versus Division Ring Hyperbolic Plane Quaternion Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References to Chapter XVI

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    C. Arf, Untersuchungen über quadratische Formen in Körpern der Charakteristik 2, J. reine angew. Math. 183 (1941), 148–167.MathSciNetGoogle Scholar
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    F. Bolli, Verallgemeinerung des Verbands von Glauser, Master’s Thesis, University of Zurich 1977.Google Scholar
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    H.R. Glauser, Quadratische Formen in unendlichdimensionalen Vektorräumen im Falle von Charakteristik 2, Ph. D. Thesis, University of Zurich 1976.Google Scholar
  4. [4]
    H. Gross, Untersuchungen über quadratische Formen in Körpern der Charakteristik 2, J. reine angew. Math. 297 (1978), 80–91.MathSciNetzbMATHGoogle Scholar

References to Appendix I

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    J. Dieudonné, Sur les groupes classiques. ASI 1040, Hermann Paris, 1958.Google Scholar
  2. [2]
    I. Kaplansky, Quadratic forms. J. Math. Soc. Japan 5 (1953) 200–207.zbMATHGoogle Scholar
  3. [3]
    H.A. Keller, Algebras de cuaternios y formas cuadrâticas sobre campos de caracteristica 2. Notas matemâticas, Universidad Católica de Chile-Santiago, 8 (1978) 65–84.Google Scholar
  4. [4]
    T.Y. Lam, The algebraic Theory of quadratic forms. W.A. Benjamin Inc., Reading Massachusetts, 1973.Google Scholar
  5. [5]
    J. Tits, Formes quadratiques, groupes orthogonaux et algèbres de Clifford. Invent. math. 5 (1968) 19–41.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Herbert Gross
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichZürichSwitzerland

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