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

Degree of fields query

  1. Apr 10, 2012 #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. Apr 10, 2012 #2
    ....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?