Algebraic Number Theory
《Algebraic Number Theory》 · 第 34–35 页 · Chapter I，Section 6「The Class Number」
In order to count the ideals $\mathfrak a\ne0$ of the ring $\mathcal O_K$ we consider their absolute norm $\mathcal N(\mathfrak a)=(\mathcal O_K:\mathfrak a)$. […] The proposition immediately implies the multiplicativity $\mathcal N(\mathfrak a\mathfrak b)=\mathcal N(\mathfrak a)\mathcal N(\mathfrak b)$ of the absolute norm.