Definitions from Wiktionary (nilpotent)

▸ adjective:  (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
▸ adjective:  (mathematics, algebra) 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.
▸ adjective:  (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
▸ adjective:  (Lie theory, of a Lie algebra) Such that the lower central series terminates.
▸ adjective:  (group theory, of a group) Admitting a central series of finite length.
▸ adjective:  (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
▸ adjective:  (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
▸ adjective:  (of an algebra over a commutative ring) 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.
▸ noun:  (algebra) A nilpotent element.




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