Nilpotent

In mathematics, an element ${\displaystyle x}$ of a ring ${\displaystyle R}$ is called nilpotent if there exists some positive integer ${\displaystyle n}$ such that ${\displaystyle x^{n}=0}$. The smallest such ${\displaystyle n}$ is called the index of nilpotency or the degree of nilpotency of ${\displaystyle x}$.

The term, along with its sister idempotent, was introduced by Benjamin Peirce in the context of his work on the classification of algebras.