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Problem 54 (We Know $\left<p(x) \right>$ Is Maximal Iff $p(x)$ Is Irreducible)
Let $F$ be a field and let $p(x)\in F[x]$. Prove that $\left<p(x) \right>$ is a maximal ideal if and only if $p(x)$ is irreducible over $F$.
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