Prove that R is a PID (principal ideal domain) when R is a ring such that Z [tex]\subset[/tex] R [tex]\subset[/tex] Q (Z=integers, Q=rationals)
The Attempt at a Solution
So I'm not really sure how to start this problem. I know that a principal ideal domain is an integral domain in which every ideal is principal. Z is euclidean domain and therefore a PID, Q is a field and therefore a PID. So R is 'between' 2 PIDs. Also if I could show it was a Euclidean Domain then it would be a PID.