nilpotent (English, adj)
expansion: nilpotent (not comparable)
Senses:
topics: algebra
mathematics
sciences
qualifier: ring theory
glosses: Such that, for some positive integer n, xⁿ = 0.
tags: not-comparable
raw_tags: of an element x of a ring
topics: algebra
mathematics
sciences
glosses: 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).
qualifier: Lie theory
tags: not-comparable
raw_tags: of an element x of a Lie algebra L
topics: algebra
mathematics
sciences
glosses: 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.
qualifier: Lie theory
tags: not-comparable
raw_tags: of a Lie algebra
topics: algebra
group-theory
mathematics
sciences
glosses: 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.
tags: not-comparable
raw_tags: of a group
topics: algebra
mathematics
sciences
glosses: 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.
qualifier: ring theory
tags: not-comparable
raw_tags: of an ideal I
topics: algebra
mathematics
sciences
glosses: 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.
qualifier: semigroup theory
tags: not-comparable
raw_tags: of a semigroup with zero
topics: algebra
mathematics
sciences
glosses: 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.
tags: not-comparable
raw_tags: of an algebra over a commutative ring
Forms: