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Loading... The Classical Fields: Structural Features of the Real and Rational Numbers (edition 2007)by H. Salzmann
Work InformationThe Classical Fields: Structural Features of the Real and Rational Numbers by Helmut Salzmann
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"The book gives a comprehensive treatment of the classical number fields Q and R from almost every conceivable point of view: algebraic (additive and multiplicative groups, fields), order theoretic, topological, measure theoretic." Belongs to Series
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. No library descriptions found. |
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Google Books — Loading... GenresMelvil Decimal System (DDC)512.74Natural sciences and mathematics Mathematics Algebra Number theory Algebraic Number TheoryLC ClassificationRatingAverage: No ratings.Is this you?Become a LibraryThing Author. |