nilpotent.
Such that, for some positive integer n, xⁿ = 0.
Meaning & usage
Such that, for some positive integer n, xⁿ = 0.
If a square matrix is upper triangular and has zeros on the diagonal, then it is nilpotent (under the usual matrix multiplication).
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. Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
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. Such that the lower central series terminates.
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. Admitting a central series of finite length.
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. Such that there exists a natural number k with Iᵏ = 0.
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. Containing only nilpotent elements.
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. 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.
Where this word comes from
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.
A nilpotent element.
Where this word comes from
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.
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Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.