Skip to main content
Springer Nature Link
Log in

Lectures on Formally Real Fields

  • Book
  • © 1984

Overview

Authors:
  1. Alexander Prestel

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
Softcover Book USD 39.95
Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

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.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects.

Table of contents (10 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Orderings and semiorderings of fields

    • Alexander Prestel
    Pages 1-14

  3. Quadratic forms over formally real fields

    • Alexander Prestel
    Pages 15-24

  4. Real algebraic closures

    • Alexander Prestel
    Pages 25-33

  5. Some notions from model theory

    • Alexander Prestel
    Pages 34-48

  6. The transfer-principle for real closed fields

    • Alexander Prestel
    Pages 49-61

  7. The space of orderings and semiorderings

    • Alexander Prestel
    Pages 62-69

  8. Real places

    • Alexander Prestel
    Pages 70-84

  9. Real henselian fields

    • Alexander Prestel
    Pages 85-96

  10. SAP-fields

    • Alexander Prestel
    Pages 97-108

  11. Quadratic forms over formally real fields

    • Alexander Prestel
    Pages 109-118

  12. Back Matter

    Pages 119-125
    Download chapter PDF
Back to top

Accessibility Information

PDF accessibility summary

This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format.

Bibliographic Information

  • Book Title: Lectures on Formally Real Fields

  • Authors: Alexander Prestel

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0101548

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1984

  • Softcover ISBN: 978-3-540-13885-3Published: 01 November 1984

  • eBook ISBN: 978-3-540-39093-0Published: 05 January 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 128

  • Additional Information: Originally published by the Instituto de Matematica Pura e Aplicada, Rio de Janeiro

  • Topics: Algebra, Mathematical Logic and Foundations

Keywords

Publish with us

Policies and ethics

Back to top