the ring of integers of a number field is finitely generated over
Let be a number field of degree over and let be the ring of integers of . The ring is a free abelian group of rank . In other words, there exists a finite integral basis (with elements) for , i.e. there exist algebraic integers such that every element of can be expressed uniquely as a -linear combination of the .
Every ideal of is finitely generated.
Proof of the corollary.
|Title||the ring of integers of a number field is finitely generated over|
|Date of creation||2013-03-22 15:08:22|
|Last modified on||2013-03-22 15:08:22|
|Last modified by||alozano (2414)|