Is a field that never embeds twice in another field necessarily a prime field? – mathoverflow.net

Is a field that never embeds twice in another field necessarily a prime field? – mathoverflow.net

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Call a field $k$ unrepeatable$^1$ if for every field $L$ there are either zero or one field homomorphisms $k \to L$. Then the prime fields $\mathbb{Q}$ and $\mathbb{F}_p$ for $p$ prime are clearly ...

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