# Ring Theory/Idempotent and Nilpotent elements

${\displaystyle x\in R}$ is an Idempotent if ${\displaystyle x^{2}=x}$
${\displaystyle x\in R}$ is nilpotent if ${\displaystyle \exists n\in \mathbb {N} }$ such that ${\displaystyle x^{n}=0}$