Homework Statement
Let K = Q(21/4)
Determine the automorphism group Aut(K/Q)
Homework Equations
An automorphism is an isomorphism from a Field to itself
Aut(K/Q) is the group of Automorphisms from k/Q to K/Q
Definition: A K-Homomorphism from L/K to L'/K is a homomorphism...
Homework Statement
Let K = Q(21/4)
Determine the automorphism group Aut(K/Q)
Homework Equations
An automorphism is an isomorphism from a Field to itself
Aut(K/Q) is the group of Automorphisms from k/Q to K/Q
Definition: A K-Homomorphism from L/K to L'/K is a homomorphism...
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?
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...
Thanks meandonlyme ,
for b) could I put x7 - 3 into Q[X]/(X8 + 4X5 - 6X + 2)
(which is x7 - 3 still) and then calculate the number of roots in there: 1 since it is over Q.
So there is one root and hence one homomorphism.
Similarly for c) and d)
Hi,
I am trying to calculate the number of homomorphisms from one field to another:
a) F2 ---> F3
b) Q[X]/(X7 - 3) ---> Q[X]/(X8 + 4X5 - 6X + 2)
c) F7 [X] / (X2 + X - 1) ---> F7[X] / (X2 + 1)
d) Q( 21/4 ) ---> C
Attempt at a solution
a) I'm pretty sure there are no homomorphisms between F2...