# Prime Ideal

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

### Other articles related to "prime ideal, prime ideals, ideals, ideal, prime":

Prime Ideal Theorem
... In mathematics, the prime ideal theorem may be the Boolean prime ideal theorem the Landau prime ideal theorem on number fields ...
Prime Ideal - Connection To Maximality
... Prime ideals can frequently be produced as maximal elements of certain collections of ideals ... For example An ideal maximal with respect to having empty intersection with a fixed m-system is prime ... An ideal maximal among annihilators of submodules of a fixed R module M is prime ...
Regular Chain - Properties
... The saturated ideal sat(T) is an unmixed ideal with dimension n −

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