Lectures on Formally Real Fields

  • Authors
  • Alexander┬áPrestel
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1093)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Alexander Prestel
    Pages 1-14
  3. Alexander Prestel
    Pages 15-24
  4. Alexander Prestel
    Pages 25-33
  5. Alexander Prestel
    Pages 34-48
  6. Alexander Prestel
    Pages 49-61
  7. Alexander Prestel
    Pages 62-69
  8. Alexander Prestel
    Pages 70-84
  9. Alexander Prestel
    Pages 85-96
  10. Alexander Prestel
    Pages 97-108
  11. Alexander Prestel
    Pages 109-118
  12. Back Matter
    Pages 119-125

About this book

Introduction

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.

Keywords

Fields Real Fields algebra algebraic geometry model theory number theory quadratic form

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0101548
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-13885-3
  • Online ISBN 978-3-540-39093-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book