Classical Fields - Structural Features of the Real and Rational Numbers

Informationen zum Autor Helmutt Salzmann is Full Professor of Mathematics at Mathematisches Institut, Universität Tübingen, Germany. Klappentext The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational numbers are examined additionally with respect to their orderings, and these fields are compared to their non-standard counterparts. Typical substructures and quotients, relevant automorphism groups and many counterexamples are described. Also discussed are completion procedures of chains and of ordered and topological groups, with applications to classical fields. The p-adic numbers are placed in the context of general topological fields: absolute values, valuations and the corresponding topologies are studied, and the classification of all locally compact fields and skew fields is presented. Exercises are provided with hints and solutions at the end of the book. An appendix reviews ordinals and cardinals, duality theory of locally compact Abelian groups and various constructions of fields. Zusammenfassung The classical fields are the real! rational! complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive text studies these underlying structures and analyzes their interactions and interdependencies. Exercises! hints and solutions are provided. Inhaltsverzeichnis Preface; 1. Real numbers; 2. Non-standard numbers; 3. Rational numbers; 4. Completion; 5. The p-adic numbers; 6. Appendix; Hints and solutions; Bibliography; Notation; Index.

Product details

• Authors: T. (Bayerische-Julius-Maximilians-Universitat Wurzburg Grundhoefer, T. Grundhofer, T. Grundhöfer, H. Hahl, H. (Universitat Stuttgart) Hahl, H. Hähl, R. (Technische Universitat Carolo Wilhelmina zu Braunschweig Loewen, R. Lowen, H. Salzmann, H. (Eberhard-Karls-Universitat Tubingen Salzmann, Helmut Salzmann, Helmut Grundhofer Salzmann
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 23.08.2007
• EAN: 9780521865166
• ISBN: 978-0-521-86516-6
• No. of pages: 418
• Series: Encyclopedia of Mathematics and Its Applications; Encyclopedia of Mathematics an; Encyclopedia of Mathematics and its Applications; Encyclopedia of Mathematics an
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra