Ramification index of a prime ideal
= Ramification index of a prime ideal
{title2=$e_{\mathfrak p}$}
If $\mathfrak p$ is a prime ideal of $\mathcal O_K$ above a rational prime $p$, its ramification index is the exponent $e_{\mathfrak p}$ of $\mathfrak p$ in the factorization of $(p)$. Equivalently, for the normalized ideal valuation, $e_{\mathfrak p}=v_{\mathfrak p}(p)$.