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    Isomorphism from Z7[x] to Z

    Homework Statement Let R = Z7[x]. Show that R is not isomorphic to Z. Homework Equations 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...