Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By johng

Math Help - Z modules and exact sequences

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Z modules and exact sequences

    Find an example of a short exact sequence of Z-modules that does not split.
    Any hints?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jan 2013
    From
    Europe
    Posts
    4
    Thanks
    1

    Re: Z modules and exact sequences

    0 \to \mathbb Z \to\mathbb Q \to \mathbb{Q/Z} \to 0. It is clearly a short exact sequence of abelian group and \text{Hom}_\mathbb{Z}(\mathbb{Q/Z}, \mathbb{Q})=0, since \mathbb{Q/Z} is torsion while \mathbb Q is torsion-free.
    Last edited by Curu; January 16th 2013 at 08:48 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    712
    Thanks
    298

    Re: Z modules and exact sequences

    The above answer was posted as I was writing the following different example, but I'll post it anyway.
    Z modules and exact sequences-exactsequence.png
    Thanks from Deveno
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: September 21st 2011, 01:12 AM
  2. Short exact sequences
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: December 7th 2010, 06:19 PM
  3. Why are exact ODEs called exact?
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: December 27th 2009, 10:48 AM
  4. exact sequence of modules
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 30th 2009, 06:49 AM
  5. short exact sequences
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 17th 2008, 10:31 AM

Search Tags


/mathhelpforum @mathhelpforum