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:
“Faith in reason as a prime motor is no longer the criterion of the sound mind, any more than faith in the Bible is the criterion of righteous intention.”
—George Bernard Shaw (1856–1950)
“In one sense it is evident that the art of kingship does include the art of lawmaking. But the political ideal is not full authority for laws but rather full authority for a man who understands the art of kingship and has kingly ability.”
—Plato (428–348 B.C.)