# Math Help - 2 Ring Isomorphism Questions

1. ## 2 Ring Isomorphism Questions

1.) Determine all ring isomorphisms from Zn to itself.

2.) Determine all ring homomorphisms from Z+Z into Z+Z (where + is the Direct Product).

For #1, I know that Zn has unity 1, so phi(1) = 1. Does that mean Phi(x) = x is the only ring isomorphism from Zn to itself?

I'm really stuck on #2. Any help would be greatly appreciated.

If $\phi(1) = 1$ then $\phi(n) = \phi(1+...+1) = \phi(1) + ... + \phi(1) = n\phi(1) = n$.
Hint: If you know what $\phi(1,0)$ and $\phi(0,1)$ is then you can determine everything.