Niel Shell

Topological Fields and Near Valuations (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 248
• Erscheinungstermin: 23. Juni 2021
• Englisch
• ISBN-13: 9781000447521
• Artikelnr.: 61915154

Autorenporträt

Niel Shell (City University of New York)

Inhaltsangabe

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