# To find all Ring homomorphisms from $\mathbb Z_m$ to $\mathbb Z_n$ [duplicate]

How to find all Ring homomorphisms from $\mathbb Z_m$ to $\mathbb Z_n$ (with the usual ring structure ) ?

• This is surely a duplicate... – Sal Dec 3 '14 at 5:59
• Note that by the usual definition, all ring homomorphisms map the identity of one ring to the identity of the other. – Omnomnomnom Dec 3 '14 at 6:02
• See this. – jdoicj Dec 3 '14 at 6:05
• (The weaker requirement of ring homomorphism allows for a more interesting consideration; if you really insist on ring homomorphisms, see the comment by Omnom... above). – user147263 Dec 3 '14 at 6:21