Valued Fields

1. Auflage. Softcover version of original hardcover Auflage 2005
ISBN: 978-3-642-06345-9
Verlag: Springer

Buch, Englisch, 208 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 335 g

Reihe: Springer Monographs in Mathematics

Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.

Zielgruppe

Research

Autoren/Hrsg.

Engler, Antonio J.

Prestel, Alexander

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Absolute Values.- Valuations.- Extension of Valuations.- Henselian Fields.- Structure Theory.- Applications of Valuation Theory.

Leseproben

Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.