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


Corollary 1.

Let E/K be a Galois extensionMathworldPlanetmath of fields, let F/K be an arbitrary extension and assume that E and F are both subfieldsMathworldPlanetmath of some other larger field T. The compositum of E and F is here denoted by EF. Then [EF:F]=[E:EF].

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