1. The problem statement, all variables and given/known data Hello guys So I have the following problem, given the mapping above I have to check weather it's ring homomorphism, and maybe monomorphism or epimorphism. 3. The attempt at a solution So the mapping is obviously well defined, and I have proven it's homomorphism, and it's obviously not monomorphism because a polynomial P(x)= 5 - x2 is in the kernel so kernel is not trivial. I am not sure how to prove if the function is surjective or not, obviously if the codomain were integers for every integers C , I could just use constant function p(x) = C and function would be surjective.