Proof that Let char K p 0 and assume F K(u,v) where u P K, vP EK and F K p 2 Then F is not a simple extension of K Exhibit an infinite number of intermediate fields ...

To prove that F is not a simple extension of K and to exhibit an infinite number of intermediate fields we can make use of Galois theory First lets as ...

Proof that Let char K = p 0 and assume F = K(u,v) where u P

Question:

Proof that Let char K = p ≠ 0 and assume F = K(u,v) where u^P ϵ K, vP EK and [F: K] = p². Then F is not a simple extension of K. Exhibit an infinite number of intermediate fields.

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