1
Number Fields
▶
1.1
Recap on rings and fields
1.2
Irreducible polynomials
1.3
Field extensions
1.4
Algebraic numbers and number fields
1.5
Embeddings
1.6
The standard representation
1.7
Norm and Trace
2
Algebraic integers
▶
2.1
Rings of integers
2.2
Discriminants
2.3
Cyclotomic fields
3
Factorization in rings of integers
▶
3.1
Units
3.2
Ideals in rings of integers
3.3
Dedekind domains
3.4
Norms of ideals
3.5
Splitting of prime ideals
3.6
Embeddings and prime ideals
4
The ideal class group
▶
4.1
Computing class groups
5
Solving Diophantine equations
6
Geometry of numbers
7
Bibliography
Dependency graph
Algebraic Number Theory
Christopher Birkbeck
1
Number Fields
1.1
Recap on rings and fields
1.2
Irreducible polynomials
1.3
Field extensions
1.4
Algebraic numbers and number fields
1.5
Embeddings
1.6
The standard representation
1.7
Norm and Trace
2
Algebraic integers
2.1
Rings of integers
2.2
Discriminants
2.3
Cyclotomic fields
3
Factorization in rings of integers
3.1
Units
3.2
Ideals in rings of integers
3.3
Dedekind domains
3.4
Norms of ideals
3.5
Splitting of prime ideals
3.6
Embeddings and prime ideals
4
The ideal class group
4.1
Computing class groups
5
Solving Diophantine equations
6
Geometry of numbers
7
Bibliography