Uniqueness of splitting fields

  • #1
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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?
 

Answers and Replies

  • #2
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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?
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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