nilpotent
a. [数] 幂(为)零的
发音
词形变化
释义与例句
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1.
A nilpotent element.
数学
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1.
Such that, for some positive integer n, xⁿ = 0.
数学If a square matrix is upper triangular and has zeros on the diagonal, then it is nilpotent (under the usual matrix multiplication).
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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.
Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
数学 -
3.
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.
数学 -
4.
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.
数学 -
5.
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.
数学 -
6.
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.
数学 -
7.
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.
数学
词源
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.
来源：wiktionary