Nilpotence
Nilpotence in algebra refers to an element a of a ring R such that a^n = 0 for some positive integer n. The least such n, if it exists, is called the nilpotency index of a. The zero element is nilpotent with index 1. Nilpotent elements are annihilated by some power, and this property is preserved under taking powers.
In matrix theory, a nilpotent matrix N satisfies N^k = 0 for some k. Over a field, such
In commutative algebra, the set Nil(R) of all nilpotent elements in a ring R is called the
For general rings, nilpotent elements always satisfy a^n = 0, and they lie in the Jacobson radical