I Uniqueness of splitting fields

1. Jan 25, 2017

PsychonautQQ

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. Jan 25, 2017

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.