Introduction / Chapter 1: |
Integral Extensions / 1.1: |
Localization / 1.2: |
Norms, Traces and Discriminants / Chapter 2: |
Norms and traces / 2.1: |
The Basic Setup for Algebraic Number Theory / 2.2: |
The Discriminant / 2.3: |
Dedekind Domains / Chapter 3: |
The Definition and Some Basic Properties / 3.1: |
Fractional Ideals / 3.2: |
Unique Factorization of Ideals / 3.3: |
Some Arithmetic in Dedekind Domains / 3.4: |
Factorization of Prime Ideals in Extensions / Chapter 4: |
Lifting of Prime Ideals / 4.1: |
Norms of ideals / 4.2: |
A Practical Factorization Theorem / 4.3: |
The Ideal Class Group / Chapter 5: |
Lattices / 5.1: |
A Volume Calculation / 5.2: |
The Canonical Embedding / 5.3: |
The Dirichlet Unit Theorem / Chapter 6: |
Preliminary Results / 6.1: |
Statement and Proof of Dirichlet's Unit Theorem / 6.2: |
Units in Quadratic Fields / 6.3: |
Cyclotomic Extensions / Chapter 7: |
Some Preliminary Calculations / 7.1: |
An Integral Basis of a Cyclotomic Field / 7.2: |
Factorization of Prime Ideals in Galois Extensions / Chapter 8: |
Decomposition and Inertia Groups / 8.1: |
The Frobenius Automorphism / 8.2: |
Applications / 8.3: |
Local Fields / Chapter 9: |
Absolute Values and Discrete Valuations / 9.1: |
Absolute Values on the Rationals / 9.2: |
Artin-Whaples Approximation Theorem / 9.3: |
Completions / 9.4: |
Hensel's Lemma / 9.5: |
Appendices |
Quadratic Reciproicty Via Gauss Sums / A: |
Extension of Absolute Values / B: |
The Different / C: |
Solutions to Problems |
Index |
Introduction / Chapter 1: |
Integral Extensions / 1.1: |
Localization / 1.2: |