Let E/F be an algebraic extension and let K and L be intermediate fields (i.e. F...

Let E/F be an algebraic extension and let K and L be intermediate fields (i.e. F ⊆ K ⊆ E and F ⊆ L ⊆ E). Assume that [K : F] and [L : F] are finite and that at least K/F or L/F is Galois. Prove that [KL : F] = [K : F][L : F] / [K ∩ L : F] .

Expert Solution

let E/F be an algebraic extension and let K and L be intermediate fields.

Colby Messinger answered 2 years ago

Theorem: Let K/F be a field extension and let a ∈ K be algebraic over F....

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