Results 1 to 2 of 2

Thread: nonzero torsion elements

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    23

    nonzero torsion elements

    If $\displaystyle R$ has zero divisors show that every nonzero $\displaystyle R-$module has nonzero torsion elements.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by zelda2139 View Post
    If $\displaystyle R$ has zero divisors show that every nonzero $\displaystyle R-$module has nonzero torsion elements.
    so there exist nonzero elements $\displaystyle r,s \in R$ such that $\displaystyle rs=0.$ let $\displaystyle M \neq (0)$ be an R-module and $\displaystyle 0 \neq m \in M.$ if $\displaystyle sm=0,$ then we're done. so suppose $\displaystyle m'=sm \neq 0.$ then: $\displaystyle rm'=(rs)m=0. \ \ \Box$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding nonzero matrices that result in AB=0
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Apr 11th 2011, 01:32 PM
  2. IBVP with a nonzero BCs
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Sep 26th 2010, 05:23 AM
  3. Let C* be the set of all nonzero complex numbers a+bi
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Mar 17th 2010, 05:45 PM
  4. Non-torsion elements
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Jun 8th 2009, 11:44 PM
  5. Nonzero numbers? (587)
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Sep 22nd 2008, 10:15 PM

Search Tags


/mathhelpforum @mathhelpforum