Ideal Norm
In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an ideal in a less complicated ring. When the less complicated number ring is taken to be the ring of integers, Z, then the norm of a nonzero ideal I of a number ring R is simply the size of the finite quotient ring R/I.
Read more about Ideal Norm: Relative Norm, Absolute Norm
Famous quotes containing the words ideal and/or norm:
“For most Northerners, Texas is the home of real men. The cowboys, the rednecks, the outspoken self-made right-wing millionaires strike us as either the best or worst examples of American manliness.... The ideal is not an illusion nor is it contemptible, no matter what damage it may have done. Many people who scorn it in conversation want to submit to it in bed. Those who believe machismo reeks of violence alone choose to forget it once stood for honor as well.”
—Edmund White (b. 1940)
“As long as male behavior is taken to be the norm, there can be no serious questioning of male traits and behavior. A norm is by definition a standard for judging; it is not itself subject to judgment.”
—Myriam Miedzian, U.S. author. Boys Will Be Boys, ch. 1 (1991)