# Isomorphism from Z7[x] to Z

## Homework Statement

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

## 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.