nilpotent /nɪlˈpəʊtənt/adjective 8noun 1forms 1 adjective8 •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). •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). •Such that the lower central series terminates. •Admitting a central series of finite length. •Such that there exists a natural number k with Iᵏ = 0. •Containing only nilpotent elements. •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. noun1 •A nilpotent element. formsnilpotents
