Results 1 to 2 of 2

Math Help - Modules

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    97

    Modules

    Let R be a ring. prove that if M is a free R-module, then Ann_R M =0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

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

    Let R be a ring. prove that if M is a free R-module, then Ann_R M =0.
    let r \in \text{ann}_R M and choose x \in M to be in a basis of M. then rx=0 and thus r=0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modules
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: June 6th 2011, 11:18 AM
  2. Modules over P.I.D
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 18th 2011, 05:28 AM
  3. FG-modules
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 12th 2009, 04:50 AM
  4. Modules
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 30th 2009, 02:17 AM
  5. Modules
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 5th 2009, 04:23 PM

Search Tags


/mathhelpforum @mathhelpforum