Prime ideal
Ideal in a ring which has properties similar to prime elements / From Wikipedia, the free encyclopedia
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This article is about ideals in ring theory. For prime ideals in order theory, see Ideal (order theory) § Prime ideals.
Not to be confused with Primary ideal.
In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers.[1][2] The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal.
Primitive ideals are prime, and prime ideals are both primary and semiprime.