Let $R$ be an integral domain and $a$ be a nonzero non unit of $R$. Recall that:
(i) $a$ is called irreducible if whenever $a=bc$ for some $b, c\in R$, then $b$ or $c$ is a unit.
(ii) $a$ is prime if whenever $a|bc$ for some $b, c\in R$, then $a|b$ or $a|c$.
Note that every prime element is irreducible.
Which of the following is true about $R$?