# Definition(s) > [!NOTE] Definition (Prime Element of Integral Domain) \[MA268\] > Let $(D,+,\times)$ be an [[Integral Domain|integral domain]]. We say that $x\in D$ is irreducible iff $x$ is non-zero; $x$ is not a [[Unit in a Ring|unit]]; and for all $a,b\in D$ if $x$ [[Divisibility|divides]] $ab$ then $x$ divides at least one of $a$ and $b$. # Properties # Reference(s)