Results 1 to 2 of 2

Math Help - Transcendental

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    58

    Transcendental

    Let F be an extension field of K. Let a ∈ F be algebraic over K, and let t ∈ F be transcendental over K. Show that a+t is transcendental over K.

    I am completely lost. Can anyone help at all? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,201
    Thanks
    1789
    Use a proof by contradiction. Let x= a+ t. If x is NOT transcendental, it satisfies some polynomial equation, P(x)= 0, with coefficients in K. Then P(a+ t)= 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. transcendental numbers
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 10th 2011, 03:42 PM
  2. Replies: 7
    Last Post: April 14th 2010, 08:09 AM
  3. Transcendental number
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 13th 2010, 04:35 PM
  4. Transcendental
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 24th 2009, 12:26 PM
  5. Purely Transcendental
    Posted in the Advanced Algebra Forum
    Replies: 11
    Last Post: August 13th 2007, 06:14 PM

Search Tags


/mathhelpforum @mathhelpforum