Let F₂(t) denote the field of rational functions in t over F₂. (a) Prove that F₂(³√t)/F₂(t) is not Galois. (b) Prove that

Question

Let F₂(t) denote the field of rational functions in t over F₂.
(a) Prove that F₂(³√t)/F₂(t) is not Galois.
(b) Prove that F4(³√t)/F4(t) is Galois.                                                  
(c) For which values of n is F₂n(³√t)/F₂n (t) Galois? Justify your answer.

Kunduz · Accepted Answer

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