- Finitely generated abelian groups
- Commutative Algebra

- Rings of Algebraic Integers

- Unique Factorization of Ideals

- Computing

- Factoring Primes

- Chinese Remainder Theorem

- Discrimannts, Norms, and Finiteness of the Class Group
- Preliminary Remarks
- Discriminants
- Norms of Ideals
- Finiteness of the Class Group via Geometry of Numbers

- Computing Class Groups

- Dirichlet's Unit Theorem
- The Group of Units
- Finishing the proof of Dirichlet's Unit Theorem
- Some Examples of Units in Number Fields
- Preview

- Decomposition and Inertia Groups

- Decomposition Groups and Galois Representations

William Stein 2004-05-06