Determining extension fields

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Reference no: EM13117721

Please answer the following:

Let f(x) = x^p - alpha E F [x] be irreducible, and let alpha be a root of f in an extension field. Show that if F (alpha)/F is a Galois extension, then g(x) = x^p - 1 splits in the field F.

Reference no: EM13117721

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