# Multiplicative Set

Let $S$ be a multiplicative set of $R$, and write $S^{-1}R$ for the ring of $S-$ fractions of $R$. Prove that the two functors $S^{-1}(\cdot)$ and $S^{-1}R \oplus_{R}(\cdot)$ from the category of $R$ modules to that of $S^{-1}R$ module are isomorphic.