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I Uniqueness of splitting fields

  1. Jan 25, 2017 #1
    So if E and E' are both extensions of K so that both E and E' are splitting fields of different families of polynomials in K[x], then E and E' are not isomorphic, correct? They need to be splitting fields for the same family of polynomials in K[x], correct?
  2. jcsd
  3. Jan 25, 2017 #2


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    Staff: Mentor

    I don't think so, at least not in this generality. They could still have the same zeros although the sets might be different. I think one has to consider the ideal generated by the two families.
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