Let $R$ be an integral domain.

Define what is meant by the field of fractions $F$ of $R$. [You do not need to prove the existence of $F$.]

Suppose that $\phi: R \rightarrow K$ is an injective ring homomorphism from $R$ to a field $K$. Show that $\phi$ extends to an injective ring homomorphism $\Phi: F \rightarrow K$.

Give an example of $R$ and a ring homomorphism $\psi: R \rightarrow S$ from $R$ to a ring $S$ such that $\psi$ does not extend to a ring homomorphism $F \rightarrow S$.