# Definition(s) > [!NOTE] Definition (Irreducible Element of a Ring) \[MA268\] > 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 $x=ab$ then either $a\in D^*$ or $b\in D^*$ where $D^*$ denotes the [[Unit Group of Ring|unit group]] of $D$. > [!Example] > See [[Irreducible Polynomial]]. # Properties # References