Lecture Notes in Mathematics

Lectures on Formally Real Fields

Authors: Prestel, A.

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About this book

Absolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization.

In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.

Table of contents (10 chapters)

  • Orderings and semiorderings of fields

    Prestel, Alexander

    Pages 1-14

  • Quadratic forms over formally real fields

    Prestel, Alexander

    Pages 15-24

  • Real algebraic closures

    Prestel, Alexander

    Pages 25-33

  • Some notions from model theory

    Prestel, Alexander

    Pages 34-48

  • The transfer-principle for real closed fields

    Prestel, Alexander

    Pages 49-61

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-540-39093-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-3-540-13885-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Formally Real Fields
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1093
Copyright
1984
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-39093-0
DOI
10.1007/BFb0101548
Softcover ISBN
978-3-540-13885-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XI, 128
Additional Information
Originally published by the Instituto de Matematica Pura e Aplicada, Rio de Janeiro
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