The Classical Fields : Structural Features of the Real and Rational Numbers
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| Title: | The Classical Fields : Structural Features of the Real and Rational Numbers |
|---|---|
| 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. |
| Authors: | H. Salzmann, T. Grundhöfer, H. Hähl, R. Löwen |
| Resource Type: | eBook. |
| Subjects: | Number theory, Numbers, Real, Numbers, Rational |
| Categories: | MATHEMATICS / Algebra / General, MATHEMATICS / Number Theory, MATHEMATICS / Topology |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Classical Fields : Structural Features of the Real and Rational Numbers – Name: Abstract Label: Description Group: Ab Data: 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22H%2E+Salzmann%22">H. Salzmann</searchLink><br /><searchLink fieldCode="AR" term="%22T%2E+Grundhöfer%22">T. Grundhöfer</searchLink><br /><searchLink fieldCode="AR" term="%22H%2E+Hähl%22">H. Hähl</searchLink><br /><searchLink fieldCode="AR" term="%22R%2E+Löwen%22">R. Löwen</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numbers%2C+Real%22">Numbers, Real</searchLink><br /><searchLink fieldCode="DE" term="%22Numbers%2C+Rational%22">Numbers, Rational</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Algebra+%2F+General%22">MATHEMATICS / Algebra / General</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Number+Theory%22">MATHEMATICS / Number Theory</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Topology%22">MATHEMATICS / Topology</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 512.74 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Number theory Type: general – SubjectFull: Numbers, Real Type: general – SubjectFull: Numbers, Rational Type: general Titles: – TitleFull: The Classical Fields : Structural Features of the Real and Rational Numbers Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: H. Salzmann – PersonEntity: Name: NameFull: T. Grundhöfer – PersonEntity: Name: NameFull: H. Hähl – PersonEntity: Name: NameFull: R. Löwen – PersonEntity: Name: NameFull: H. Salzmann – PersonEntity: Name: NameFull: T. Grundhöfer – PersonEntity: Name: NameFull: H. Hähl – PersonEntity: Name: NameFull: R. Löwen IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2007 – D: 04 M: 02 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9780521865166 – Type: isbn-electronic Value: 9781107398863 – Type: isbn-electronic Value: 9781461941514 Numbering: – Type: volume Value: 00112 Titles: – TitleFull: The Classical Fields : Structural Features of the Real and Rational Numbers Type: main |
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