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The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112)

H. Salzmann
4.9/5 (27247 ratings)
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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 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112). To get started finding The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112), you are right to find our website which has a comprehensive collection of manuals listed.
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0521865166

The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112)

H. Salzmann
4.4/5 (1290744 ratings)
Read Now Download now ⏭ listen AudioBook
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 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112). To get started finding The Classical Fields: Structural Features of the Real and Rational Numbers (Encyclopedia of Mathematics and its Applications, Series Number 112), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
Pages
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Format
PDF, EPUB & Kindle Edition
Publisher
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Release
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ISBN
0521865166

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