A Dedekind domain is a UFD iff its ideal class group is trivial

Let be a Dedekind domain. Then is a UFD iff the ideal class group is trivial. #m/thm/ring

check

If the ideal class group is trivial, then all ideals are principal, so is a PID and thus UFI translates to the UFD property.

#state/tidy | #lang/en | #SemBr