# $\mathbb{Q}$-automorphisms of $\mathbb{R}$

What is a $\mathbb{Q}$-automorphisms of $\mathbb{R}$ ? Does this mean, I have to think if $\mathbb{R}$ as a $\mathbb{Q}$ vector space ? Or does that mean, that it is an automorphism on $\mathbb{R}$ that restricted to $\mathbb{Q}$ is the identity (this was some definition I picked up on the web, searching for an explanation)?

And can someone please tell me how I could find all of these automorphisms ?

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What is the context? – Julian Kuelshammer Nov 6 '12 at 22:29

It's probably a field automorphism of $\mathbb R$. Any such automorphism automatically is the identity when restricted to $\mathbb Q$.
Amy field automorphism of $\mathbb R$ is the identity on all of $\mathbb R$. – GEdgar Nov 6 '12 at 22:52