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Question: abstract algebra let be a tower of field extensions with...

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Abstract Algebra

Let F\subseteq K\subseteq L be a tower of field extensions with [L:F] finite, and let  \alpha \in L with p(x)=m_{\alpha,F}(x) the minimal polynomial of  \alpha over F.

Prove that K \otimes_F F(\alpha)\cong {K[x]\over (p(x))} as K-algebras.

(Please DO NOT COPY another Zookal or Stackexchange solution)

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