Nilpotent

In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that xn = 0. In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that xn = 0. The term was introduced by Benjamin Peirce in the context of his work on the classification of algebras. No nilpotent element can be a unit (except in the trivial ring {0}, which has only a single element 0 = 1). All non-zero nilpotent elements are zero divisors. An n-by-n matrix A with entries from a field is nilpotent if and only if its characteristic polynomial is tn. If x is nilpotent, then 1 − x is a unit, because xn = 0 entails