Solution
= Solution
Assume that $p$ is a <prime element>. If $p=ab$, then $p$ divides $ab$, so $p$ divides $a$ or $b$. If $p\mid a$, write $a=pc$; cancellation in the <integral domain> gives $1=bc$, so $b$ is a <unit>. The other case is symmetric. Hence every prime element is <irreducible element>[irreducible].