I have a question about the proof of corollary 4.12. in Eisenbuds "Commutative Algebra with a view towards Algebraic Geometry":
If $R$ is a normal domain, then any monic irreducible polynomial in $R[x]$ is prime.
I understand the argument in the proof except one detail: naturally $R[x]/(f)$ is a free $R$-module, and letting $Q$ be the field of fractions of $R$, it's claimed that the injection $R[x]/(f) \to Q \otimes R[x]/(f)$ a monomorphism. Why is it necessarily a monomorphism? Maybe the reason I'm confused is because I'm not sure how an element of $R[x]/(f)$ is mapped to $Q \otimes R[x]/(f)$.