nilpotent

名词 n. 形容词 adj.
中文释义

英文释义

名词 n.
  1. A nilpotent element.
    — The so-called spinor algebra of C(2), the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra of space, including its beautiful representation on the Riemann sphere, and a new proof of the Heisenberg uncertainty principle.
形容词 adj.
  1. Such that, for some positive integer n, xⁿ = 0. not-comparable
    — If a square matrix is upper triangular and has zeros on the diagonal, then it is nilpotent (under the usual matrix multiplication).
  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). not-comparable
  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. not-comparable
  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. not-comparable
  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. not-comparable
  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. not-comparable
  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. not-comparable

词形变化

nilpotents plural

词汇关系

衍生词
nilpotent algebra nilpotent ideal nilpotently nilpotent orbit nilpotent semigroup quasinilpotent
相关词
nilpotence nilpotency idempotent nullipotent unipotent
并列词
idempotent

词源

词源 1
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.
词源 2
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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