adjective Such that, for some positive integer n, x = 0.
If a square matrix is upper triangular and has zeros on the diagonal, then it is nilpotent (under the usual matrix multiplication).
adjective 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 I = 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.
adjective Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
adjective Such that the lower central series terminates.
adjective Admitting a central series of finite length.
adjective Such that there exists a natural number k with I = 0.
adjective Containing only nilpotent elements.
adjective 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.