corollary to the compositum of a Galois extension and another extension is Galois
(Corollary)
Corollary 1Let $E/K$ 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 $[EF:F] =
[E:E\cap F]$ .
This follows immediately from item (2) of the theorem.
"corollary to the compositum of a Galois extension and another extension is Galois" is owned by rm50.
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