ideal classes form an abelian group
where are ideals of .
We shall check the group properties:
Then is a group under the operation .
It is abelian since .
This is group is called the ideal class group of . The ideal class group is one of the principal objects of algebraic number theory. In particular, for an arbitrary number field , very little is known about the size of this group, called the class number of . See the analytic class number formula.
|Title||ideal classes form an abelian group|
|Date of creation||2013-03-22 12:49:40|
|Last modified on||2013-03-22 12:49:40|
|Last modified by||mathcam (2727)|
|Defines||ideal class group|