# Isomorphism from Z7[x] to Z

1. Nov 7, 2013

### jouiswalker

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.

2. Nov 7, 2013

### jouiswalker

Actually nevermind, it is that easy. There's a hint hidden that basically says "an isomorphism has to be one to one..."