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June 18th, 2008, 06:37 AM  #1 
Newbie Joined: Jun 2008 Posts: 1 Thanks: 0  Degree of an extension
Given the polynomial f(t)=t^4  2 over Q, and L the splitting field of f, how does one determine the degree of the extension L:Q? If anyone could help me out with this i would be very appreciated.Thank you. 
June 24th, 2008, 09:58 PM  #2 
Member Joined: Dec 2006 Posts: 39 Thanks: 0  Re: Degree of an extension
Obviously s:= 2^(1/4) is a root, and the other ones are s*w, with w a 4th root of unity in C ==> if we put w = i, then the roots are s, s*w= s*i, s*w^2 = s, and s*w^3 = s*i. Now Q(s,i) is clearly the splitting field of the pol. over Q, and you can write Q <= Q(s) <= Q(s,i), and thus you can now calculate the extension's degree. Regards Tonio 

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