Discriminant root field (reviewed)

If $K/F$ is a finite algebraic extension, it can be defined by a polynomial $f(x)\in F[x]$. The polynomial discriminant, $\mathrm{disc}(f)$, is well-defined up a factor of a non-zero square. The discriminant root field of the extension is $F(\sqrt{\mathrm{disc}(f)})$, which is well-defined.

If $n=[K:F]$, then the Galois group $G$ for $K/F$ is a subgroup of $S_n$, well-defined up to conjugation. The discriminant root field can alternatively be described as the fixed field of $G\cap A_n$.