nilpotent
Such that, for some positive integer n, xⁿ = 0Such that, for some positive integer n, xⁿ = 0.
Meaning
7 senses(not comparable)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.
(not comparable)Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
(not comparable)Such that the lower central series terminates.
(not comparable)Admitting a central series of finite length.
(not comparable)Such that there exists a natural number k with Iᵏ = 0.
(not comparable)Containing only nilpotent elements.
(not comparable)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.
- equal to zero when raised to a certain power
Translations
3 languagesBy meaning 1
Origin
From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” -From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens.
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