Ideal Norm

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:

    blind wantons like the gulls who scream
    And rip the edge off any ideal or dream.
    Louis MacNeice (1907–1963)

    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)