In algebra (which is a branch of mathematics), a **prime ideal** is a subset of a ring which shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number or zero.

Primitive ideals are prime, and prime ideals are both primary and semiprime.

Read more about Prime Ideal: Prime Ideals For Commutative Rings, Prime Ideals For Noncommutative Rings, Important Facts, Connection To Maximality

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