1. The problem statement, all variables and given/known data Show that a f: Z → R , n → n*1R is a homomorphism of rings 2. Relevant equations 3. The attempt at a solution I'm not sure how to exactly go about answering this question, but I'm going to try to start with the definition: f(a+b) = f(a) + f(b) f(a*b) = f(a) * f(b) f(1Z) = 1R Ok, so if I actually have a clue what the problem statement means -- which is just slightly possible -- then this function maps values 'n' to 'n' times the identity unit of R. Which is equal to the identity unit of Z, so I think that part of the definition is more-or-less covered. How do I go about using the first two parts of the definition? The function is just f(n) = n right? so do I just sub in (a+b) for n? f(a+b) = f(a) + f(b) ??? Is there anyway I can actually show that this is the case? I mean isn't this intuitive/properly defined upon the integers? same for the other part f(ab) = f(a)*f(b) ..... i'm just not sure how to actually show this... thanks for any help.