I was looking through this question, and there's a thing I don't understand why it holds. I mean the next statement in the answer by @Peter McNamara:
Since $R$ is Noetherian, $I$ is finitely presented, so $\mathrm{Hom}(,−)$ commutes with direct limits ...
I don't understand why this holds, I've tried to either prove or google it, but I've failed, although it looks like an exercise. It seems like somehow the finite presentation plays the crucial role, but I don't see it.
There's also a comment under the answer with the same question that remained unanswered. Can anyone give a hint why this holds? Thanks!