Definition of "nilpotent" in English

adjective

1. (mathematics, algebra, ring theory, of an element x of a ring) 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).

2. (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.

noun

1. (algebra) A nilpotent element.