Different in a tower
= Different in a tower
For finite separable extensions $L/E/K$,
$$
\mathfrak D_{L/K}
=\mathfrak D_{L/E}\mathfrak D_{E/K}\mathcal O_L.
$$
For normalized valuations this says
$$
d(L/K)=d(L/E)+e(L/E)d(E/K).
$$
= Different in a tower
For finite separable extensions $L/E/K$,
$$
\mathfrak D_{L/K}
=\mathfrak D_{L/E}\mathfrak D_{E/K}\mathcal O_L.
$$
For normalized valuations this says
$$
d(L/K)=d(L/E)+e(L/E)d(E/K).
$$