Local Fields
《Local Fields》 · 第 14 页 · Chapter I，Section 4「Extensions」
On the other hand, if $\mathfrak P$ divides $\mathfrak p$, the field $B/\mathfrak P$ is an extension of the field $A/\mathfrak p$. As $B$ is finitely generated over $A$, $B/\mathfrak P$ is an extension of $A/\mathfrak p$ of finite degree. The degree of this extension is called the residue degree of $\mathfrak P$ in the extension $L/K$, and is denoted $f_{\mathfrak P}$. Thus: $f_{\mathfrak P}=[B/\mathfrak P:A/\mathfrak p]$.