1. Nov 26, 2011 #1

   ae1709

   

   Let
   \begin{equation}
   {F}\subseteq{K_i}\subseteq{E}
   \end{equation}
   for i = 1,...,r with E a finite extension of F and where the intermediate fields \begin{equation} K_i \end{equation}are each normal extensions of F for all i.
   
   Define:
   \begin{equation}
   L = \{f(a_1,....,a_r) : [f]\in{F[x]}, [a_i]\in[K_i]\}
   \end{equation}
   
   1) Prove that L is a subfield of E and contains \begin{equation} K_i \end{equation} for all i.
   
   2) Prove that L is a normal extension of F.
   
   I really need help with this. Thanks

    

   ae1709, Nov 26, 2011
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3. Nov 28, 2011 #2

   micromass

   

   Insights Author

   So, what did you try already?? (1) shouldn't be too difficult. It's just checking that something is a field...

    

   micromass, Nov 28, 2011

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