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The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112) - Hardcover
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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Book Description
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.
About the Author
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.
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date2007
- ISBN 10 0521865166
- ISBN 13 9780521865166
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages418
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The Classical Fields: Structural Features of the Real and Rational Numbers. Encyclopedia of Mathematics and Its Applications, 112.
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The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112)
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THE CLASSICAL FIELDS: STRUCTURAL FEATURES OF THE REAL AND RATIONAL NUMBERS (ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS)
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The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112)
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The Classical Fields: Structural Features of the Real and Rational Numbers (Hardcover)
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Hardcover. Condition: new. Hardcover. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521865166
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