Lectures on Formally Real Fields

by A. Prestel

Overview

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.

Product Details

ISBN-13:	9783540138853
Publisher:	Springer Berlin Heidelberg
Publication date:	12/03/1984
Series:	Lecture Notes in Mathematics , #1093
Edition description:	1984
Pages:	128
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Orderings and semiorderings of fields.- Quadratic forms over formally real fields.- Real algebraic closures.- Some notions from model theory.- The transfer-principle for real closed fields.- The space of orderings and semiorderings.- Real places.- Real henselian fields.- SAP-fields.- Quadratic forms over formally real fields.