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:
“We have reason to be grateful for celestial phenomena, for they chiefly answer to the ideal in man.”
—Henry David Thoreau (1817–1862)
“To be told that our child’s behavior is “normal” offers little solace when our feelings are badly hurt, or when we worry that his actions are harmful at the moment or may be injurious to his future. It does not help me as a parent nor lessen my worries when my child drives carelessly, even dangerously, if I am told that this is “normal” behavior for children of his age. I’d much prefer him to deviate from the norm and be a cautious driver!”
—Bruno Bettelheim (20th century)