The Stacks project

Example 15.115.2. Let $k$ be a perfect field of characteristic $p > 0$. Let $A = k[[x]]$ and $K = k((x))$. Let $B = A[x^{1/p}]$. Any weak solution $K_1/K$ for $A \to B$ is inseparable (and any finite inseparable extension of $K$ is a solution). We omit the proof.