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.

单词	Absolute norm
释义	Absolute norm 原声例句 Sophie's World A Novel About the History of Philosophy As you can imagine, the wandering Sophists created bitter wrangling in Athens by pointing out that there were no absolute norms for what was right or wrong. 可以想象，四处游荡的诡辩者指出，对与错没有绝对的标准，从而在雅典引发了激烈的争论。英语百科 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.
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Absolute norm

Ideal norm