Results 1 to 3 of 3

Math Help - Algebra

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    10

    Algebra

    Please help me solving these problems. Thanks in advance.

    a) find the degree of a minimal splitting field of (x^6 + 1) over Q.

    b) if a is a any algebraic number prove that there exists a positive integer 'n' such that 'na' is an algebraic number.

    c) if W is a subspace of V and vєV satisfies (v,w) + (w,v) = (w,w) for all wєW prove that (v, w)=0 for all wєW where V is inner product space over F.

    d) if T1,T2 є Hom(V,W), then show that
    1) r(α(T1))=r(T1) for all αєF, α≠0
    2) | r(T1)-r(T2) | ≤ r(T1+T2) ≤ r(T1) +r(T2), where r(T) means rank of T.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by mslghlg View Post

    Please help me solving these problems. Thanks in advance.
    so many questions and not even one line work from you!


    a) find the degree of a minimal splitting field of (x^6 + 1) over Q.
    find the roots of x^6=-1 and then find the smallest field which contains the roots and \mathbb{Q}. your final answer is \mathbb{Q}(i,\sqrt{3}).


    b) if a is a any algebraic number prove that there exists a positive integer 'n' such that 'na' is an algebraic number.
    are you sure they don't want you to prove that na is an algebraic integer not just an algebraic number, which trivially is if you let n = 1.


    c) if W is a subspace of V and vєV satisfies (v,w) + (w,v) = (w,w) for all wєW prove that (v, w)=0 for all wєW where V is inner product space over F.
    is the field F here supposed to be the field of real or complex numbers? in either case noting that (w,w) \geq 0 and changing w to -w in your identity will solve the problem.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    10
    "if a is a any algebraic number prove that there exists a positive integer 'n' such that 'na' is an algebraic integer"
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 4th 2011, 09:39 AM
  2. Replies: 2
    Last Post: December 6th 2010, 04:03 PM
  3. Algebra or Algebra 2 Equation Help Please?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 12th 2010, 12:22 PM
  4. Replies: 0
    Last Post: April 24th 2010, 12:37 AM
  5. algebra 2 help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 4th 2009, 07:24 PM

Search Tags


/mathhelpforum @mathhelpforum