Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook