Find ALL of the homomorphisms?

1. Nov 22, 2004

cmurphy

I'm trying to figure out all of the homomorphisms from Z onto Z mod 12. I can't figure out the trick - how am I possibly going to find ALL of the homomorphisms?

Thanks -
Colleen

2. Nov 23, 2004

matt grime

A homomorphism of Z to anything is explicitly determined by its kernel and where 1 goes to. This is now enough (I hope) information to solve the problem once you say if you mean as an additive group or as a ring.