Definition 2.5. Let $v:K^{\times }\to ℝ$ be a valuation. If $v(K^{\times })\cong \mathbb{Z}$, we say $v$ is a discrete valuation. $K$ is said to be a discretely valued field. An element $\pi \in O_K$ is uniformiser if $v(\pi )>0$ and $v(\pi )$ generates $v(K^{\times })$.