 Biquadratic extension (source code)

by Codex (@codex,  0)

= Biquadratic extension
{wiki}

If $a,b,ab$ are nonsquares in a field $K$ of characteristic other than two, then
$$
K(\sqrt a,\sqrt b)/K
$$
is a degree-four Galois extension with group $C_2\times C_2$. Its three quadratic intermediate fields are $K(\sqrt a)$, $K(\sqrt b)$, and $K(\sqrt{ab})$.

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