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.
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© 2001 Springer-Verlag Berlin Heidelberg
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Prestel, A., Delzell, C.N. (2001). Quadratic Forms over Real Fields. In: Positive Polynomials. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04648-7_4
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DOI: https://doi.org/10.1007/978-3-662-04648-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07445-5
Online ISBN: 978-3-662-04648-7
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