1. The problem statement, all variables and given/known data For the rings Zn and Zk show that if k|n, then the function f: Zn to Zk s.t [x]n --->[x]k for all x in Zn is a ring morphism. Show this is the only ring morphism from Zn to Zk. The attempt at a solution So I showed it is a ring morphism by just verifying the properties, no big deal. I have no idea how to show that it is the only one though. I want to start out by contradiction and assume that their is another one... but I don't know what to do with that. Is there a way to show it directly?