Hello everybody, I'm a bit stuck here. I have a problem tha goes like this: Let R be a principal ideal domain (PID). Let D a subset of R which is multiplicatively closed. Show that the ring of quotients D^(-1)R is a PID too. I've tried several different ways but I couldn't get to the result. For example, take an ideal I of D^(-1)R. I was able to show that all r \in R such as r/d \in I for some d \in D, form an ideal of R, (Thus a principal ideal). If I could show that I=(a)/d for some d.. Anyway, I don't know.. Any hints for that? Thank you in advance!