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Theorem: Let K/F be a field extension and let a ? K be algebraic over F....

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Advance Math

Theorem: Let K/F be a field extension and let a ? K be algebraicover F. If deg(mF,a(x)) = n, then

1. F[a] = F(a).

2. [F(a) : F] = n, and

3. {1, a, a2 , ..., an?1} is a basis for F(a).

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