Primitive ideals are prime, and prime ideals are both primary and semiprime. ==Prime ideals for commutative rings== An ideal {mvar|P} of a commutative ring {mvar|R} is prime if it has the following two properties: This generalizes the following property of prime numbers: if p is a prime number and if p divides a product ab of two integers, then p ...
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http://en.wikipedia.org/wiki/Prime_ideal
an ideal in a ring with a multiplicative identity, having the property that when the product of two elements of the ring results in an element of the ideal, at least one of the elements is an element of the ideal.
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https://www.infoplease.com/dictionary/prime-ideal
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