nipotent

An element a of a ring is nilpotent is aⁿ = 0_R for some positive integer n.

Some interesting characteristics related to ring
R has no nonzero nilpotent elements if and only if 0_R is the unique solution of the equation x² = 0_R.

Let a and b be nilpotent elements in a commutative R. a + b and ab are also nilpotent.

Let N be the set of all nilpotent elements of R. N is a subring of R.