Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Need help proving L is a normal exension of F.

  1. Nov 26, 2011 #1
    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
     
  2. jcsd
  3. Nov 28, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    So, what did you try already?? (1) shouldn't be too difficult. It's just checking that something is a field...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Need help proving L is a normal exension of F.
  1. F→∏ A l Z (Replies: 1)

Loading...