1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Torsion-free modules

  1. Jan 25, 2009 #1
    Hi all, I came across this problem in a book and I can`t seem to crack it.
    It says that if we have an integral domain R and M is any non-principal ideal of R,
    then
    M is torsion-free of rank 1 and is NOT a free R-module.

    Why is this true?

    cheers
     
  2. jcsd
  3. Jan 25, 2009 #2
    ah so i see why it needs to be torsion free. (M lies in R, so if there is r such that rm=0, R cant be an integral domain...)

    but what about the rank? Why must it be 1? I am also surprised that it is not free..
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Torsion-free modules
  1. About a torsion module (Replies: 2)

  2. Free R-modules (Replies: 1)

Loading...