Ideal norm

Summary

Let $\mathfrak{a}$ be a nonzero ideal in the ring of integers $\mathcal{O}_K$ of a number field. The norm of $\mathfrak{a}$ is the number of elements of the quotient ring $\mathcal{O}_K / \mathfrak{a}$. It is multiplicative, and for a principal ideal it is the absolute value of the field norm of a generator. It measures the size of an ideal. It is used in the finiteness of the class number and in the definition of the Dedekind zeta function.