Definition:Nilpotent

Definition

Nilpotent Ring Element

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

An element $x \in R$ is nilpotent if and only if:

$\exists n \in \Z_{>0}: x^n = 0_R$

Nilpotent Matrix

Let $\mathbf A$ be a square matrix over a number field.

$\mathbf A$ is described as nilpotent if and only if $\mathbf A^n = \mathbf 0$ for some $n \in \Z_{>0}$.

Also see

• Results about nilpotence can be found here.