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Definition of normal extension

  1. Aug 27, 2010 #1
    normal extension - an algebraic field extension L/K is said to be normal if L is the splitting field of a family of polynomials in K[X]. (wikipedia)

    I have a question about the 'family of polynomials'
    it says the family should be arbitarary large?
    if E be an algebraic closure of Q(rational number).
    is E a normal extension of Q?
  2. jcsd
  3. Aug 29, 2010 #2
    What is the splitting field of all polynomials with coefficients in Q? If you can show that this is E, then you have shown that E/Q is a normal extension.
  4. Aug 30, 2010 #3
    Yes, I got it.
    You mean arbitrary large family is admittable.

    Thanks a lot !
  5. Aug 30, 2010 #4
    Yes the family can be arbitrarily large.
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