Proposition 6.12. Assuming that:

$L ∕ K$ finite extension of complete discretely valued fields.
(i): $O_{K}$ is compact.
(ii): The extension of residue fields $k_{L} ∕ k$ is finite and separable.

Then there exists

α \in O_{L}

such that

O_{L} = O_{K} [α]

.