Question
Suppose that $F$ is a field and there is a ring homomorphism from $Z$ onto $F$. Show that $F$ is isomorphic to $Z_{p}$ for some prime $p$.
Step 1
Let $\phi: \mathbb{Z} \to F$ be a ring homomorphism from the integers to the field $F$. Since $\phi$ is onto, every element of $F$ can be written as $\phi(n)$ for some integer $n$. Show more…
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