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:
“The prime purpose of being four is to enjoy being four—of secondary importance is to prepare for being five.”
—Jim Trelease (20th century)
“The unique eludes us; yet we remain faithful to the ideal of it; and in spite of sense and of our merely abstract thinking, it becomes for us the most real thing in the actual world, although for us it is the elusive goal of an infinite quest.”
—Josiah Royce (1855–1916)