# corollary to the compositum of a Galois extension and another extension is Galois

###### Corollary 1.

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 $[EF:F]=[E:E\cap F]$.

This follows immediately from item (2) of the theorem.

Title corollary to the compositum of a Galois extension and another extension is Galois CorollaryToTheCompositumOfAGaloisExtensionAndAnotherExtensionIsGalois 2013-03-22 18:42:04 2013-03-22 18:42:04 rm50 (10146) rm50 (10146) 4 rm50 (10146) Corollary msc 12F99 msc 11R32