# Isomorphism between quotient fields of polynomial rings [closed]

Let $$R$$ be an integral domain and $$F$$ be its field of fractions. If $$X$$ is a nonempty set, prove that there is a ring monomorphism from $$R[X]$$ to $$F[X]$$ that extends to an isomorphism of their quotient fields.

## closed as off-topic by Saad, caverac, Namaste, Cesareo, user416281 Dec 2 '18 at 14:49

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• Integral domain means defining $Frac(R)$ is easy, and $R[X]$ is again an integral domain. – reuns Dec 2 '18 at 6:11
• I recommend that you take a look at our guide for new askers. While that guide is mostly targeting freshmen and high schoolers, it does apply to all (and it is not kosher to discriminate based on the level anyway). – Jyrki Lahtonen Dec 2 '18 at 8:36