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manuscripta mathematica

, Volume 29, Issue 2–4, pp 295–303 | Cite as

Quadratic forms over formally real fields with eight square classes

  • Mieczysław Kula
  • Lucyna Szczepanik
  • Kazimierz Szymiczek
Article

Abstract

Complete classification of formally real fields with 8 square classes with respect to the behaviour of quadratic forms is given. Two fields F and K are equivalent with respect to quadratic forms if the quadratic form schemes of the two fields are isomorphic or in other words, if the Witt rings W(F) and W(K) are isomorphic. It is shown here that for formally real fields with 8 square classes there are exactly seven possible quadratic form schemes and for each of the seven schemes a formally real field with 8 square classes and the given scheme is constructed.

Keywords

Quadratic Form Number Theory Algebraic Geometry Topological Group Form Scheme 
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

  1. [1]
    CORDES, C.M.: The Witt group and the equivalence of fields with respect to quadratic forms. J. Algebra26, 400–421 (1973)Google Scholar
  2. [2]
    CORDES, C.M.: Quadratic forms over non-formally real fields with a finite number of quaternion algebras. Pacific J. Math.63, 357–366 (1976)Google Scholar
  3. [3]
    KULA, M.: Fields with non-trivial Kaplansky's radical and finite square class number. Acta Arith. (to appear)Google Scholar
  4. [4]
    KULA, M.: Fields with prescribed quadratic form schemes. Math. Zeit. (to appear)Google Scholar
  5. [5]
    PFISTER, A.: Quadratische Formen in beliebigen Körpern. Invent. Math.1, 116–132 (1966)Google Scholar
  6. [6]
    SZYMICZEK, K.: Quadratic forms over fields with finite square class number. Acta Arith.28, 195–221 (1975)Google Scholar
  7. [7]
    SZYMICZEK, K.: Quadratic forms over fields. Dissertationes Math.152, 1–67 (1977)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Mieczysław Kula
    • 1
  • Lucyna Szczepanik
    • 1
  • Kazimierz Szymiczek
    • 1
  1. 1.Institute of MathematicsSilesian UniversityKatowicePoland

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