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.