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

Corollary 1.

Let $E\mathrm{/}K$ be a Galois extension of fields, let $F\mathrm{/}K$ 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 $E\mathit{}F$. Then $\mathrm{[}EF\mathrm{:}F\mathrm{]}\mathrm{=}\mathrm{[}E\mathrm{:}E\mathrm{\cap }F\mathrm{]}$.

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

Title	corollary to the compositum of a Galois extension and another extension is Galois
Canonical name	CorollaryToTheCompositumOfAGaloisExtensionAndAnotherExtensionIsGalois
Date of creation	2013-03-22 18:42:04
Last modified on	2013-03-22 18:42:04
Owner	rm50 (10146)
Last modified by	rm50 (10146)
Numerical id	4
Author	rm50 (10146)
Entry type	Corollary
Classification	msc 12F99
Classification	msc 11R32