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Quadratic Forms over Real Fields

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

Abstract

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.

Keywords

Quadratic Form Prime Ideal Positive Cone Real Field Transcendence Degree 
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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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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