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Thread: Automorphisms of Q

  1. April 10th 2008, 07:44 PM #1
    syme.gabriel
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    Automorphisms of Q

    How can you prove that any automorphism of \mathbb{Q} (\sqrt[3]{2}) leaves \mathbb{Q} fixed?
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  2. April 10th 2008, 08:03 PM #2
    ThePerfectHacker
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    Quote Originally Posted by syme.gabriel View Post
    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.
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