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:
“Ay, look: high heaven and earth ail from the prime foundation;
All thoughts to rive the heart are here, and all are vain:
Horror and scorn and hate and fear and indignation—
Oh, why did I awake? When shall I sleep again?”
—A.E. (Alfred Edward)
“Plato—who may have understood better what forms the mind of man than do some of our contemporaries who want their children exposed only to “real” people and everyday events—knew what intellectual experience made for true humanity. He suggested that the future citizens of his ideal republic begin their literary education with the telling of myths, rather than with mere facts or so-called rational teachings.”
—Bruno Bettelheim (20th century)