1. The problem statement, all variables and given/known data Let R be any ring and f:Z→R a homomorphism. a)Show that f is completely determined by the single value f(1) b)Determine all possible homomorphisms f in the case when R = Z. 2. Relevant equations 3. The attempt at a solution This question has me totally confused. I have gone through all the properties of homororphisms in the book but i am still confused.How is the homomorphism completely determined by one value anyway?