ABSTRACT
Let’s return to Example 19.10. 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 was onto, and so R[x]/〈x2 +1〉 is isomorphic to the field C. We would like to find out what sort of ideal leads to a ring of cosets that is a field.
