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.
Thanks in advance!