Timeline for Automorphisms of $\mathbb{C}$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2012 at 22:41 | history | edited | Daniel Miller | CC BY-SA 3.0 |
fixed an error.
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| Apr 4, 2012 at 22:20 | comment | added | zeb | For arbitrary fields k this isn't true... for instance, take h to be any nontrivial real algebraic extension of the rationals, and k to be the reals. (There are also counterexamples if k is taken to be the p-adic numbers, for any prime p.) I think it does extend to any algebraically closed k, though. | |
| Apr 4, 2012 at 22:16 | comment | added | Emil Jeřábek | It certainly does not work for arbitrary fields. For example, let $h=\mathbb Q(\sqrt 2)$, $k=\mathbb Q(\sqrt[4]2)$, and $f$ the automorphism of $h$ such that $f(\sqrt2)=-\sqrt2$. It works when $k$ is algebraically closed, as explained in the comments above. | |
| Apr 4, 2012 at 21:46 | history | answered | Daniel Miller | CC BY-SA 3.0 |