Semiprime ring

A Hasse diagram of a portion of the lattice of ideals of the integers Z. The purple and green nodes indicate semiprime ideals. The purple nodes are prime ideals, and the purple and blue nodes are primary ideals.

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 $n\mathbb Z$ where n is a square-free integer. So, $30\mathbb Z$ is a semiprime ideal of the integers, but $12\mathbb Z\,$ is not.

单词	Semiprime ring
释义	Semiprime ring 英语百科 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 $n\mathbb Z$ where n is a square-free integer. So, $30\mathbb Z$ is a semiprime ideal of the integers, but $12\mathbb Z\,$ is not.
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