Lectures on Formally Real Fields / by Alexander Prestel.

Format:

Book

Author/Creator:

Prestel, A. (Alexander), 1941- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1093.

Lecture Notes in Mathematics, 0075-8434 ; 1093

Language:

English

Subjects (All):

Algebra.

Logic, Symbolic and mathematical.

Mathematical Logic and Foundations.

Local Subjects:

Algebra.

Mathematical Logic and Foundations.

Physical Description:

1 online resource (XI, 128 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1984.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783540390930

Access Restriction:

Restricted for use by site license.