edit: deleted post.
f: R----> F
f(x)=0 for all x in R.
this is trivial homomorphism i guess. Is this acceptable to you??
Thanks guys. I was just confused because in my notes a ring homomorphism was defined from a ring to a field, and then after this was proved to be a ring isomorphism, he showed that the initial ring was actually a field. But this should arise from the fact we have a ring isomorphism. I would type out the specific example but Latex is borked