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Topological Fields and Near Valuations de Niel Shell

Topological Fields and Near Valuations: Chapman & Hall/CRC Pure and Applied Mathematics

Autor Niel Shell
en Limba Engleză Hardback – 12 iun 1990
Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory.
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Specificații

ISBN-13: 9780824784126
ISBN-10: 082478412X
Pagini: 248
Dimensiuni: 210 x 280 x 21 mm
Greutate: 0.59 kg
Ediția:New.
Editura: CRC Press
Colecția CRC Press
Seria Chapman & Hall/CRC Pure and Applied Mathematics

Locul publicării:Boca Raton, United States

Public țintă

Professional

Cuprins

PART I: SURVEY OF TOPOLOGICAL FIELDS 1 INTRODUCTION 1.1 Neighborhood Bases at Zero 1.2 Alternate Axiomatizations 1.3 Basic Properties 2 VALUATIONS AND OTHER EXAMPLES 2.1 Prevaluations 2.2 Examples of Valued Fields 3 THE LATTICE OF RING TOPOLOGIES 3.1 Lattices of Topologies . . . 3.2 Weakening Ring Topologies 3.3 Minimal Topologies 3.4 Independence 4 LOCALLY BOUNDED FIELDS 4.1 Bounded Sets 4.2 Locally Bounded Rings 4.3 Preorders 4.4 Preorders and Topologies 4.5 Lattice Results 5 NORMED FIELDS 5.1 Norms 5.2 Nilpotence and Normability 6 COMPLETENESS 6.1 Completions of Rings 6.2 Completions of Fields 7 EMBEDDING AND EXTENSION 7.1 The Problem 7.2 The Product Topology Extension 8 EXISTENCE OF FIELD TOPOLOGIES 9 CONNECTED FIELDS 10 DISCONNECTED FIELDS 10.1 Extremally Disconnected Fields 10.2 Ultraregular Fields . 11 LINEAR FIELDS PART 11: VALUED FIELDS 12 ABSOLUTE VALUES 12.1 Nonarchimedean Absolute Values 12.2 Absolute Values on PID's 12.3 Equivalent Absolute Values 12.4 Equivalent Valuations 12.5 Powers of Absolute Values 13 PLACES 14 VECTOR SPACES AND STRICTLY MINIMAL FIELDS .14.1 Strictly Minimal Fields .14.2 Completeness and Norms 14.3 Normed Algebras 15 EXTENSIONS OF VALUATIONS 15.1 Existence of Extensions 15.2 Archimedean Absolute Values 15.3 Complete and Algebraically Closed Fields . 16 CHARACTERIZATIONS 16.1 Topologies Induced by Absolute Values 16.2 Archimedean Valuations 16.3 Type V Fields 16.4 Addiator Sequences 16.5 Topologies Induced by Valuations

Notă biografică

Niel Shell (City University of New York)

Descriere

Part I (eleven chapters) of this text for graduate students provides a Survey of topological fields, while Part II (five chapters) provides a relatively more idiosyncratic account of valuation theory. No exercises but a good number of examples; appendices support the author in his intent, which ha