# Automorphisms of Q

• April 10th 2008, 08:44 PM
syme.gabriel
Automorphisms of Q
How can you prove that any automorphism of $\mathbb{Q} (\sqrt[3]{2})$ leaves $\mathbb{Q}$ fixed?
• April 10th 2008, 09:03 PM
ThePerfectHacker
Quote:

Originally Posted by syme.gabriel
How can you prove that any automorphism of $\mathbb{Q} (\sqrt[3]{2})$ leaves $\mathbb{Q}$ fixed?

The automorphism of any field leaves its prime subfield fixed. Since Q is the prime subfield, it says fixed.

If you do not like that proof, I have another one.