Valued Fields

  • Antonio J. Engler
  • Alexander Prestel

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-X
  2. Pages 1-3
  3. Pages 5-24
  4. Pages 25-56
  5. Pages 85-112
  6. Pages 113-148
  7. Back Matter
    Pages 173-205

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 acquired 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.


Galois theory Henselization algebra number theory p-adic fields ramification theory ultraproduct valuation

Authors and affiliations

  • Antonio J. Engler
    • 1
  • Alexander Prestel
    • 2
  1. 1.Departamento de MatemáticaIMECC-UNICAMPCampinasBrazil
  2. 2.Fak. Mathematik, Fachbereich Mathematik und StatistikKonstanzGermany

Bibliographic information