Field theory MOC

Intermediate field extension

Suppose 𝐹 :𝐿 :𝐾 is a tower of field extensions

𝐹|𝐿|𝐾

Then in particular one has a Vector space over a field extension, whence

[𝐹:𝐾]=[𝐹:𝐿][𝐿:𝐾]

and 𝐹 :𝐾 is finite iff both 𝐹 :𝐿 and 𝐿 :𝐾 are. field

Corollaries of this corollary

1. Given a tower 𝐹 :𝐿 :𝐾, it follows both [𝐹 :𝐾] and [𝐹 :𝐿] divide [𝐹 :𝐾].

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