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Full Product Details

Author:   A. Weiss
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Dimensions:   Width: 14.00cm , Height: 1.60cm , Length: 21.60cm
Weight:   0.318kg
ISBN:  

9780486401898

ISBN 10:   0486401898
Pages:   288
Publication Date:   29 January 1998
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

Preface; References Chapter 1. Elementary Valuation Theory 1.1 Valuations and Prime Divisors 1.2 The Approximation Theorem 1.3 Archimedean and Nonarchimedean Prime Divisors 1.4 The Prime Divisors of Q 1.5 Fields with a Discrete Prime Divisor 1.6 e and f 1.7 Completions 1.8 The Theorem of Ostrowski 1.9 Complete Fields with Discrete Prime Divisor; Exercises Chapter 2. Extension of Valuations 2.1 Uniqueness of Extensions (Complete Case) 2.2 Existence of Extensions (Complete Case) 2.3 Extensions of Discrete Prime Divisors 2.4 Extensions in the General Case 2.5 Consequences; Exercises Chapter 3. Local Fields 3.1 Newton's Method 3.2 Unramified Extensions 3.3 Totally Ramified Extensions 3.4 Tamely Ramified Extensions 3.5 Inertia Group 3.6 Ramification Groups 3.7 Different and Discriminant; Exercises Chapter 4. Ordinary Arithmetic Fields 4.1 Axioms and Basic Properties 4.2 Ideals and Divisors 4.3 The Fundamental Theorem of OAFs 4.4 Dedekind Rings 4.5 Over-rings of O 4.6 Class Number 4.7 Mappings of Ideals 4.8 Different and Discriminant 4.9 Factoring Prime Ideals in an Extension Field 4.10 Hilbert Theory; Exercises Chapter 5. Global Fields 5.1 Global Fields and the Product Formula 5.2 Adeles, Ideles, Divisors, and Ideals 5.3 Unit Theorem and Class Number 5.4 Class Number of an Algebraic Number Field 5.5 Topological Considerations 5.6 Relative Theory; Exercises Chapter 6. Quadratic Fields 6.1 Integral Basis and Discriminant 6.2 Prime Ideals 6.3 Units 6.4 Class Number 6.5 The Local Situation 6.6 Norm Residue Symbol Chapter 7. Cyclotomic Fields 7.1 Elementary Facts 7.2 Unramified Primes 7.3 Quadratic Reciprocity Law 7.4 Ramified Primes 7.5 Integral Basis and Discriminant 7.6 Units 7.7 Class Number Symbols and Notation; Index

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