TITLE: Is it true that an integral domain $R$ is a UFD if and only if intersection of any two principal ideals of $R$ is principal ?
QUESTION [5 upvotes]: Is it true that an integral domain $R$ is a UFD if and only if intersection of any two principal ideals of $R$ is principal ?

REPLY [7 votes]: A ring $R$ such that the intersection of any two principal ideals of $R$ is principal is exactly a GCD domain. And a GCD domain need not be an UFD.