Nilpotent ideal

Summary

A nilpotent ideal of a ring is a one-sided or two-sided ideal $I$ such that some power $I^n$ is zero. This means that every product of $n$ elements of $I$ vanishes, a uniform version of being a nil ideal. Every nilpotent ideal is nil, but a nil ideal need not be nilpotent. A ring is called semiprime when it has no nonzero nilpotent ideals. The Jacobson radical of a left Artinian ring is a nilpotent ideal.