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Am I right that all prime ideals in $\mathbb{Z}[x]$ has the form $p\mathbb{Z}[x]$ for some prime $p\in\mathbb{Z}$?

Thanks a lot!

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    Hint: they can't be all the primes since none of them are maximal (since modding out by them yields the non-field $\Bbb Z_p[x])$2012-09-21

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