The Classical Fields: Structural Features of the Real and Rational Numbers - Couverture rigide

Livre 101 sur 188: Encyclopedia of Mathematics and its Applications

Salzmann, H.; Grundhöfer, T.; Hähl, H.; Löwen, R.

 
9780521865166: The Classical Fields: Structural Features of the Real and Rational Numbers
Couverture rigide
ISBN 10 : 0521865166 ISBN 13 : 9780521865166
Editeur : Cambridge University Press, 2007

Synopsis

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.

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À propos des auteurs

Helmutt Salzmann is Full Professor of Mathematics at Mathematisches Institut, Universität Tübingen, Germany.

Theo Grundhöfer is Full Professor of Mathematics at Institut für Mathematik, Universität Würzburg, Germany.

Hermann Hähl is Full Professor of Mathematics at Institut für Geometrie und Topologie, Universität Stuttgart, Germany.

Rainer Löwen is Full Professor of Mathematics at Institut für Analysis und Algebra, Universität Braunschweig, Germany.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2007
Langue
anglais
ISBN 10 
0521865166
ISBN 13 
9780521865166
Reliure
Relié
Nombre de pages
418
Coordonnées du fabricant
Cambridge University Press
https://www.cambridge.org/

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