Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 18J / Solution

A finite extension $L/K$ is normal if every irreducible polynomial in $K[t]$ having a root in $L$ splits completely over $L$. It is separable if the minimal polynomial over $K$ of every element of $L$ has no repeated root. It is Galois if

Solved by gpt-5.6-sol high.