Let $F = \mathbb Q(y)$ be a field of rational functions, and $F[x]$ be polynomial ring over it.
How do I show that $f(x) = x^n - y$ is irreducible for a natural number $n$, and find a splitting field and a Galois group of $f$?
2026-04-02 06:24:57.1775111097
Galois group of polynomial over rational functions
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