Are there any homomorphisms from integers into finite rings other than modulo $n$?

Are there any homomorphisms from integers into finite rings other than
modulo $n$?

Are there any "homomorphisms" from $Z$ onto finite rings other than $Z/nZ$
? I think if instead of mapping $k$ to $k$ (mod $p$), you map it to $p -
(k$ (mod $p$)$)$ and you get $f(-ab) = f(a)f(b)$. But are there any
interesting ones?