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 $f(1) = 1$
How to prove that there are at least two different unital homomorphisms for field $K\rightarrow K$
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group-theory
field-theory
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1This is not generally true. Take K=Z_2 for instance, then there is just one homomorphism. – 2012-11-16
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0More 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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0Sorry, 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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0What examples of fields do you know? You probably know one that has 2 such homomorphisms. – 2012-11-16
1 Answers
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$K=\Bbb C$, take identity and complex conjugation.