I am doing the following exercise:
Suppose $S$ is a multiplicative set of $A$, an integral domain, and interpret $S^{-1}A = \varinjlim \dfrac{1}{s}A$, where the limit is over $s \in S$ and in the category of $A$-modules.
I thought I had an answer but I don't think I have used the fact that $A$ is an integral domain so I am skeptical of my answer now. I would appreciate an answer (with explanation where the integral domain hypothesis is used). Thanks!