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
Famous quotes containing the words prime and/or ideal:
“If one had to worry about one’s actions in respect of other people’s ideas, one might as well be buried alive in an antheap or married to an ambitious violinist. Whether that man is the prime minister, modifying his opinions to catch votes, or a bourgeois in terror lest some harmless act should be misunderstood and outrage some petty convention, that man is an inferior man and I do not want to have anything to do with him any more than I want to eat canned salmon.”
—Aleister Crowley (1875–1947)
“The ideal and the beautiful are identical; the ideal corresponds to the idea, and beauty to form; hence idea and substance are cognate.”
—Victor Hugo (1802–1885)