nilpotent

Meanings

1. Such that, for some positive integer n, xⁿ = 0.
2. In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
3. Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
4. Such that the lower central series terminates.
5. Admitting a central series of finite length.
6. Such that there exists a natural number k with Iᵏ = 0.
7. Containing only nilpotent elements.
8. Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.

1. A nilpotent element.

Etymology

From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens. Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.

Translations