Definition 13.2 (Unramified / ramified / totally ramified). The extension $L∕K$ is said to be:

• unramified if $e_{L∕K}=1$ (equivalently $f_{L∕K}=[L:K]$).

• ramified if $e_{L∕K}>1$ (equivalently $f_{L∕K}<[L:K]$).

• totally ramified if $e_{L∕K}=[L:K]$ (equivalently $f_{L∕K}=1$).