# Math Help - Ring-Homomorphisms

1. ## Ring-Homomorphisms

Find all ring-homomorphisms $\Phi: Z_n \rightarrow Z_m$

Thanks!

2. Originally Posted by roporte
Find all ring-homomorphisms $\Phi: Z_n \rightarrow Z_m$
First, $[1]_n\mapsto [1]_m$ by definition - (by definition for ring homomorphism for commutative rings).

A ring homomorphism is also a group homomorphism between $(\mathbb{Z}_n,+)$ and $(\mathbb{Z}_m,+)$. Since $[1]_n$ generates the group it means this homomorphism is completely determined by its value on this element. Can you finish it now?