The Stacks project

Lemma 15.114.2. Let $A$ be a discrete valuation ring with uniformizer $\pi $. Let $n \geq 2$. Then $K_1 = K[\pi ^{1/n}]$ is a degree $n$ extension of $K$ and the integral closure $A_1$ of $A$ in $K_1$ is the ring $A[\pi ^{1/n}]$ which is a discrete valuation ring with ramification index $n$ over $A$.

Proof. This lemma proves itself. $\square$

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