Nilpotent

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

The term, along with its sister idempotent, was introduced by Benjamin Peirce in the context of his work on the classification of algebras.^[1]