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
?