Definition 5

Let $K$ be a field, L a finite extension of $K$, $w$ a valuation on $L$, $v$ its restriction to $K$ and $\Gamma_w$ and $\Gamma_v$ their order groups. The initial index of $\Gamma_v$ in $\Gamma_w$ is called the initial ramification index of $w$ with respect to $v$ (or with respect to $K$*) and denoted by* $\varepsilon(w/v)$.

From the above corollary, $\varepsilon(w/v)$ divides $e(w/v)$ with equality in the case of a discrete valuation.