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