Homomorphism $R$-linear between $\Bbb {Z}$ and $\Bbb{Z_n}$ I was wondering how many $R$-linear homomorphisms between modules there were between $\Bbb Z$ and $\Bbb{Z_n}$. I think that the answer is "it depends on the ring" even if the exercise says "only $s(k) = 0$ for each $k\in \Bbb Z$". However, if I define $f:\Bbb Z \to \Bbb Z_n$ as $f(k) = [k]$ and $R=\Bbb Z$ with the standard $\Bbb Z$ product as extern product, this sounds like a $R$-linear homomorphism.

So the answer would be: If we do not specify the ring, then we can only assure that the zero homomorphism exists. In other cases, it depends on the ring. 

Is that correct? Could anybody please provide an example of ring in which only the null homomorphism exists?
$R=\mathbb{Z}$, since $\mathbb{Z}_n$ has torsion and $\mathbb{Z}$ doesn't, only the null homomorphism exists.
$R=\mathbb{Z}$, since $\mathbb{Z}_n$ has torsion and $\mathbb{Z}$ doesn't, only the null homomorphism exists.