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:
“The ideal and the beautiful are identical; the ideal corresponds to the idea, and beauty to form; hence idea and substance are cognate.”
—Victor Hugo (1802–1885)
“A society that presumes a norm of violence and celebrates aggression, whether in the subway, on the football field, or in the conduct of its business, cannot help making celebrities of the people who would destroy it.”
—Lewis H. Lapham (b. 1935)