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Algebraic ExtensionsLet F be a field and let E be an extension of F. We say that E is an algebraic extension of F if every Proposition 1: Let E/F be finite, Then E is algebraic over F. Proof: Let
1,,...,^{n}
of E must be linearly dependent over F, since
c_{n}^{n} + c_{n1}^{n1} + ... + c_{0} = 0.
Therefore, is algebraic over F. 
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