Degree of fields query

  1. I'm not sure if my reasoning below is correct or not.

    If a=e[itex]\stackrel{\underline{2πi}}{5}[/itex], then Q(a) = {r + sa + ta2 + ua3 +va4 : r,s,t,u,v [itex]\in[/itex] Q} . [Is this correct?]

    Then [Q(a):Q] = 5 as {1, a, a2, a3, a4} form a basis for Q(a) as a vector space over Q.

    However I am not sure if my reasoning above is correct as I have just seen a proof that [Q(a):Q] = 4 for the same a above.

    Thanks for your help.
     
  2. jcsd
  3. ....
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook