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Question

Given that `alpha` is algebraic over a finite field F of q elements, and `alpha` has a minimal polynomial m(x) of degree n, which of the folowing statements is true:
A) The degree of the minimal polynomial m(x) is always 1 , ensuring that `F(alpha)` is isomorphic to F.
B) The degree of the minimal polynomial m(x) is n, and this degree determines the dimension of `F(alpha)` as a vector space over F ?