# Math Help - Automorphisms of Q

1. ## Automorphisms of Q

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

2. 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.