I have the following problem:
"Assume $R$ is an ID. For each maximal ideal $M$ let $R_M$ be the localization $(R \ M)^{−1}R$ considered as a subset of $Frac(R)$. Show that $\cap_M R_M = R \ (⊆ Frac(R))$ where the intersection is over all maximal ideals $M$."
Was given a hint saying to take $q$ in the intersection and consider the ideal $\{r \in R; rq \in R\}$ but I am not sure how to work with these things. Can someone give me some others hints in order to make my work easier and try to explain me how to see an arbitrary element in the localization ring?
Thank you very much, everyone!
