Prove that a $UFD$ is a $PID$ if and only if every prime ideal is maximal.
I know a proof but used Zorn's lemma.Is there a proof that doesn't require Zorn's lemma?
Prove that a $UFD$ is a $PID$ if and only if every prime ideal is maximal.
I know a proof but used Zorn's lemma.Is there a proof that doesn't require Zorn's lemma?