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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** = ε-1ξε and, furthermore, εε* = 1 for some ε ∈ k.

Keywords

Division Algebra Subspace Versus Division Ring Quaternion Algebra Quadratic Space 
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References to Chapter XVI

  1. [1]
    C. Arf, Untersuchungen über quadratische Formen in Körpern der Charakteristik 2, J. reine angew. Math. 183 (1941), 148–167.Google Scholar
  2. [2]
    F. Bolli, Verallgemeinerung des Verbands von Glauser, Master’s Thesis, University of Zurich 1977.Google Scholar
  3. [3]
    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.Google Scholar

References to Appendix I

  1. [1]
    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.CrossRefGoogle Scholar
  3. [3]
    H. A. Keller, Algebras de cuaternios y formas cuadráticas sobre campos de característica 2. Notas matemáticas, 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.CrossRefGoogle 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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