This question does not let me sleep.
Fina all Ring homomorphism between Z_n----> Z_m.
I know there should be 3 case:
n>m
n<m and m=n.
the last one is trivial. Anyways, how do you guys think I should proceed or what should I consider?
I sure ..
call theta (f).
Then f(1)=1 since you assume it was a ring homomorphism. But how can we get to the point of saying that all homomorphism must be determined by f(1). There must be some cases. For instance m>n, n>m or m=n or Don't m and n have to be such that (n,m)=1. How many homomorphism can one get in each case. Are you saying they will all be determined by f(1)?