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Isomorphic abelian groups which are not isomorphic R-modules

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Give an example of two isomorphic abelian groups, which are not isomorphic R modules for some ring R.


    2. Relevant equations
    http://en.wikipedia.org/wiki/Module_(mathematics [Broken])


    3. The attempt at a solution
    I suppose we can just the same abelian group M twice, and use a different operation R x M -> M so the R modules aren't isomorphic.
    I can't think of a group M and ring R so I can find two such R-modules though.
    Any ideas?
    Thanks.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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