Definition:Nilpotent Ring Element

Definition
Let $R$ be a ring with zero $0_R$.

An element $x \in R$ is nilpotent if $x^n = 0_R$ for some (strictly) positive integer $n$.

Also see

 * Definition:Nilradical
 * Definition:Topologically Nilpotent Ring Element

Special cases

 * Definition:Nilpotent Matrix