# Galois Theory questions: Homomorphisms

1. Nov 2, 2011

### wattsup03

1. The problem statement, all variables and given/known data
Let K = Q(2^(1/4))

a) Which of the morphisms from K to C are Q(2^1/2)-homomorphisms
b) And which are K-homomorphisms?

2. Relevant equations

Theorem: There is a bijection between roots of minimal polynomial and number of homomorphisms

Definition: A K-Homomorphism from L/K to L'/K is a homomorphism L---> L' that is the identity on K

3. The attempt at a solution

Ok, I don't really understand this very well but for a) I know that there are 4 homomorphisms, since the minimal polynomial over C has four solutions and there is a bijection between the roots and the homomorphisms. What I don't understand is how I get from the number of homomorphisms to the homomorphisms themselves. If someone could explain that to me I think it would really help.

b) I can't really do b) until I know how to get the homomorphisms