Maximal and Prime Ideals

Let’s return to Example 14.5. We saw that the ring homomorphism (the evaluation homomorphism) ϕ : R[x] → C given by ϕ(f) = f(i) has kernel 〈x2 + 1〉. This homomorphism is surjective, and so R[x]/〈x2 + 1〉 is isomorphic to the field C.