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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 Ad

Szczegóły książki

Kategoria Książki po angielsku Mathematics & science Mathematics Number theory

• Pełny tytuł: Algebraic Number Theory
• Autor: A. Weiss
• Język: Angielski
• Oprawa: Miękka
• Liczba stron: 288
• EAN: 9780486401898
• ISBN: 0486401898
• ID: 02564985
• Wydawca: Dover Publications Inc.
• Waga: 360 g
• Wymiary: 217 × 142 × 12 mm
• Data wydania: 29. January 1998

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