Algebraic Number Theory
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
3 Factorization in rings of integers
We now move on to the study of primes and prime ideals 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