Quadratic Forms over Real Fields

  • Alexander Prestel
  • Charles N. Delzell
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter we give a brief introduction to the theory of quadratic forms over a field K, and to its Wittring W(K), emphasizing the case where K is real. One reason for doing so is that the Zariski spectrum of W(K) reflects the collection of orderings of K. The main reason, however, is that Pfister’s Local-Glocal Principle (3.3.11) applied to the rational function field K = ℝ(X 1,...,X n ) gives a natural generalization of Hilbert’s 17th problem in Section 3.5.


Hull Proal 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexander Prestel
    • 1
  • Charles N. Delzell
    • 2
  1. 1.Fachbereich Mathematik und StatistikUniversität KonstanzKonstanzGermany
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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