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:
“Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.”
—Charles Sanders Peirce (1839–1914)
“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)