Let be a Galois extension, and let . The trace of is defined to be the sum of all the elements of the orbit of under the group action of the Galois group on ; taken with multiplicities if is a finite extension.
In the case where is a finite extension,
The trace of is always an element of , since any element of permutes the orbit of and thus fixes .
|Date of creation||2013-03-22 12:17:59|
|Last modified on||2013-03-22 12:17:59|
|Last modified by||djao (24)|