I'm trying to understand the following Proposition:
Proposition: Let $R$ be a UFD (unique factorization domain) with subset $P$ of the set of irreducible elements of $R$. Then $P$ is in bijective correspondence with the set of minimal nonzero prime ideals of $R$, where $p \in P$ associated with the principal ideal $(p)$.
Question: Since $R$ is a UFD it is an integral domain. And in the case of integral domains the only minimal ideal is $(0)$. The above Proposition tells me that the set $P$ is in bijection with the set of minimal nonzero prime ideals of $R$. What are in this case the minimal non-zero prime ideals if I have to exclude $(0)$?