What is the minimal polynomial

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Reference no: EM13123932

Problems in Galois Theory

a. Let K be a field of characteristic p > 0, and let c in K. Show that if alpha is a root of f (x) = x^p - x - c, so is alpha + 1. Prove that K(alpha) is Galois over K with group either trivial or cyclic of order p.

b. Find all subfields of Q ( sqrt2, sqrt 3) with proof that you have them all. What is the minimal polynomial of sqrt2+ sqrt3? Which subfields does it generate over Q?

Reference no: EM13123932

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