Are there any ring homomorphisms which take $\Bbb{Q}[x]$ to $\Bbb{Z}$?
2026-04-01 02:00:28.1775008828
Finding a ring homomorphism mapping $\Bbb{Q}[x]$ to $\Bbb{Z}$
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The only ring homomorphism $\mathbb{Q}[x]\to\mathbb{Z}$ is the zero homomorphism. This is because the image of the homomorphism must be a $\mathbb{Q}$-vector space, and the only additive subgroup of $\mathbb{Z}$ that is a $\mathbb{Q}$-vector space is $\{0\}$.