Local Fields
《Local Fields》 · 第 14 页 · Chapter I，Section 4「Extensions」
Denote by $e_{\mathfrak P}$ the exponent of $\mathfrak P$ in the decomposition of $\mathfrak pB$ into prime ideals. Thus: $e_{\mathfrak P}=v_{\mathfrak P}(\mathfrak pB)$, $\mathfrak pB=\prod_{\mathfrak P\mid\mathfrak p}\mathfrak P^{e_{\mathfrak P}}$. The integer $e_{\mathfrak P}$ is called the ramification index of $\mathfrak P$ in the extension $L/K$.