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Example in Abstract Algebra

  1. Apr 3, 2008 #1
    1. The problem statement, all variables and given/known data

    I'm trying to come up with an example of a quartic polynomial over a field F which has a root in F, but whose splitting field isn't the same as its resolvent cubic.

    2. Relevant equations



    3. The attempt at a solution

    Well, I know the splitting field of the cubic resolvent is contained in the splitting field of the quartic, so that narrows down the choices quite a bit. But frankly I'm not even sure this is possible because the cubic resolvent is pretty much defined in terms of the roots of the quartic.
     
  2. jcsd
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