Is E an Algebraic Closure of Q a Normal Extension?

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An algebraic field extension L/K is normal if it serves as the splitting field for a family of polynomials in K[X]. The discussion centers on whether E, the algebraic closure of Q, qualifies as a normal extension of Q. It is confirmed that E is indeed a normal extension since it can be shown that E is the splitting field for all polynomials with coefficients in Q. The participants agree that the family of polynomials can be arbitrarily large. This understanding solidifies the classification of E/Q as a normal extension.
emptyboat
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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?
 
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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.
 
Yes, I got it.
You mean arbitrary large family is admittable.

Thanks a lot !
 
emptyboat said:
Yes, I got it.
You mean arbitrary large family is admittable.

Thanks a lot !

Yes the family can be arbitrarily large.
 
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