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单词 CorollaryToTheCompositumOfAGaloisExtensionAndAnotherExtensionIsGalois
释义

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.

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