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Math Help - Separable Extensions

  1. #1
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    Separable Extensions

    Prove that if L/G and G/F are separable algebraic extensions (not necessarily finite), then L/F is also separable.

    I could do it for the finite case, but I'm not sure what to do here?
    Last edited by gummy_ratz; December 20th 2011 at 09:06 AM.
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  2. #2
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    Re: Separable Extensions

    i don't think this is true, without more information on F. for one can devise algebraic, but not separable, extensions of F and then G, in which case L is NOT separable over F.

    perhaps F is a field of characteristic 0?
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  3. #3
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    Re: Separable Extensions

    Ohh I'm sorry, that should have said, "if L/G and G/F are *separable* algebraic extensions".

    And we already proved in class that if L/G and G/F are both algebraic extensions (not necessarily finite) then L/F is an algebraic extension. So I just need to show L/F is separable too.
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