Let $R$ be a UFD and $r\in R$ irreducible. If $S=R-(r)$, why is $S^{-1}R$ a PID?
I've finished proving the integral domain part, which was pretty easy.
How to prove it's principal? consider $R \subset S^{-1}R \subset F$, where $F$ is the field of fractions of $R$?
thank you! :p