Semiprime ring

In ring theory, a branch of mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra, semiprime ideals are also called radical ideals.

For example, in the ring of integers, the semiprime ideals are the zero ideal, along with those ideals of the form where n is a square-free integer. So, is a semiprime ideal of the integers, but is not.