Non-Archimedean place of a number field
= Non-Archimedean place of a number field
If a prime ideal $\mathfrak p$ of $K$ lies over the <prime number> $p$ with <ramification index> $e_{\mathfrak p}$, its normalized absolute value is
$$
|x|_{\mathfrak p}=p^{-\operatorname{ord}_{\mathfrak p}(x)/e_{\mathfrak p}}.
$$
It extends the usual <p-adic absolute value> on $\mathbb Q$. Its local degree is $[K_{\mathfrak p}:\mathbb Q_p]=e_{\mathfrak p}f_{\mathfrak p}$, where $f_{\mathfrak p}$ is the <residue-field degree>.