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How to prove that exists a field K such that there are two unital homomorphisms between fields $f:K\rightarrow K$? Homomorphism is unital if $f(1) = 1$

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    This is not generally true. Take K=Z_2 for instance, then there is just one homomorphism.2012-11-16
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    More generally, take $K$ to be any prime field (e.g. $\mathbb{F}_p$ or $\mathbb{Q}$). Less trivially, take $K = \mathbb{R}$.2012-11-16
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    Sorry, my fault. I've edit edited the question. To prove is that exists a field $K$ s.t. there are two unital homomorphisms in it.2012-11-16
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    What examples of fields do you know? You probably know one that has 2 such homomorphisms.2012-11-16

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$K=\Bbb C$, take identity and complex conjugation.