- #1

Daveyboy

- 58

- 0

## Homework Statement

For the rings Z

_{n}and Z

_{k}show that if k|n, then the function f: Z

_{n}to Z

_{k}

s.t [x]

_{n}--->[x]

_{k}for all x in Z

_{n}

is a ring morphism. Show this is the only ring morphism from Z

_{n}to Z

_{k}.

**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?