corollary to the compositum of a Galois extension and another extension is Galois
CorollaryToTheCompositumOfAGaloisExtensionAndAnotherExtensionIsGalois
2009-01-05 19:13:32
2009-01-05 19:13:32
Corollary
the compositum of a Galois extension and another extension is Galois
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\begin{cor} Let $E/K$ be a Galois extension of fields, let $F/K$ be an arbitrary extension and assume that $E$ and $F$ are both subfields of some other larger field $T$. The compositum of $E$ and $F$ is here denoted by $EF$. Then $[EF:F] = [E:E\cap F]$.
\end{cor}
This follows immediately from item (2) of the theorem.