Results 1 to 5 of 5

Math Help - Splitting fields

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    21

    Splitting fields

    Find the degree of the splitting field for the polynomial x^4 + 19 over the field Q(root19).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Becks View Post
    Find the degree of the splitting field for the polynomial x^4 + 19 over the field Q(root19).

    x^4+19=(x^2+\sqrt{19}\,i)(x^2-\sqrt{19}\,i) ; since the field \mathbb{Q}(\sqrt{19}) is a real field, the eement i=\sqrt{-1} is not contained in it...try to take it from here.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    21
    What do you mean by a real field?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Becks View Post
    What do you mean by a real field?

    A real field: \mathbb{Q}(\sqrt{19})\subset \mathbb{R} .

    Tonio
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2009
    Posts
    21
    Do you know what the degree would be...so once i have worked it out, i will know i have done it correctly...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Splitting fields
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 22nd 2011, 11:32 PM
  2. Splitting Fields
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 14th 2011, 12:40 PM
  3. splitting fields
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: April 5th 2010, 06:11 AM
  4. Splitting fields
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: November 19th 2009, 08:40 AM
  5. Extension fields / splitting fields proof...
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 19th 2007, 08:29 AM

Search Tags


/mathhelpforum @mathhelpforum