Results 1 to 3 of 3

Math Help - homomorphism question

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    51

    homomorphism question

    The mapping f from R* to R* (R*=set of real numbers with no zero), defined by f(x)=|x|, is a homomorphism with Ker f = {1,-1}. How would I prove that this mapping is a homomorphism? I am really struggling with this concept, any help would be great.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    Quote Originally Posted by wutang View Post
    The mapping f from R* to R* (R*=set of real numbers with no zero), defined by f(x)=|x|, is a homomorphism with Ker f = {1,-1}. How would I prove that this mapping is a homomorphism? I am really struggling with this concept, any help would be great.
    you should determine the operation on the group, or the ring if you are talking about rings
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by Amer View Post
    you should determine the operation on the group, or the ring if you are talking about rings
    It is multiplication on a group. There is no zero, and so it is not a ring and it is not addition.

    A homomorphism is a function which preserves your operation (here, it is multiplication). That is, they are functions such that f(a)f(b) = f(ab). So it does not matter if you multiply a and b together then apply the function, or if you multiply their images, you will always get the same element. These are nice, and they allow us to compare groups in a natural way.

    I would attack this problem by using that fact that |a| = \sqrt{a^2}. The solution just sort of pops out this way.
    Last edited by Swlabr; April 21st 2010 at 03:04 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Homomorphism question
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: December 3rd 2010, 05:43 AM
  2. homomorphism question
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: May 2nd 2010, 02:56 PM
  3. homomorphism question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 26th 2010, 06:25 PM
  4. Homomorphism question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 21st 2010, 08:32 PM
  5. Homomorphism question.
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 22nd 2009, 10:40 AM

Search Tags


/mathhelpforum @mathhelpforum