Next:
Finitely generated abelian groups
Up:
A BRIEF INTRODUCTION TO
Previous:
Some applications of algebraic
Contents
Index
Classical Viewpoint
Subsections
Finitely generated abelian groups
Commutative Algebra
Noetherian Rings and Modules
is Noetherian
Rings of Algebraic Integers
Rings of Algebraic Integers
Norms and Traces
Unique Factorization of Ideals
Dedekind Domains
Computing
Algorithms for Algebraic Number Theory
Using
Smith Normal Form
and Number Fields
Rings of integers
Ideals
Factoring Primes
Factoring Primes
A Method for Factoring that Often Works
A Method for Factoring that Always Works
Essential Discriminant Divisors
Chinese Remainder Theorem
The 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
An Open Problem
Computing Class Groups
Remarks on Computing the Class Group
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
Galois Extensions
Decomposition of Primes
Quadratic Extensions
The Cube Roots of Two
Decomposition Groups and Galois Representations
The Decomposition Group
Galois groups of finite fields
The Exact Sequence
Frobenius Elements
Galois Representations and a Conjecture of Artin
William Stein 2004-05-06
