page1956 Rings Matthias Lorentzen...mattegrisenforlag.com
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Question
In the proof that `F(alpha)` has `q^n` elements, which
key step ensures the bijection between elements in `F(alpha)`
and tuples `(a_0 , a_1 , ... , a_{n-1})` in vector space `F^n`,
`a_i in F`:
A) The minimal polynomial m(x) has exactly n distinct roots
in E.
B) The set `"{" 1 , alpha , alpha^2 , ... , alpha^{n-1} "}"`
forms a basis for `F(alpha)` over F
?
