proof of the ring of integers of a number field is finitely generated over
Choose any basis of over . Using the theorem in the entry multiples of an algebraic number, we can multiply each element of the basis by an integer to get a new basis with each .
Consider the group homomorphism
where is the trace (http://planetmath.org/trace2) from to . Note that is , since if and , then
where the last equality holds since .
|Title||proof of the ring of integers of a number field is finitely generated over|
|Date of creation||2013-03-22 16:03:07|
|Last modified on||2013-03-22 16:03:07|
|Last modified by||rm50 (10146)|