1. The problem statement, all variables and given/known data Let R = Z7[x]. Show that R is not isomorphic to Z. 2. Relevant equations 3. The attempt at a solution One of the necessary conditions for an isomorphism f is that f be one to one. So consider 8x in Z. f(8x) = x, f(1x) = x. So f cannot be an isomorphism. I'm clearly missing something though, since this seems a bit too easy.