# Definition(s) > [!NOTE] Definition 1 () > Let $R$ be an [[Integral Domain|integral domain]]. Then $R$ is principal ideal domain if and only if, for every [[Ideal of Ring|ideal]] $I$ of $R$, $I$ is [[Principal Ideal|principal]] (i.e. $I=aR$ for some $a\in R$). > [!Example] Example > Contents # Properties(s) # Application(s) **More examples**: # Reference(s) [^1]: Ref 1