(a) Let(R, +, ∙)and(S, ⊕, ⊙) be rings with zero elements ZR and Zs, respectively. If f: R → S is a ring homomorphism, let K = [a ∈ R | f(a) = Zs}• Prove that K is an ideal of R. (K is called the kernel of the homomorphism f.)
b) Find the kernel of the homomorphism in Example 14.19.
c) Let f, (R, +, •), and (5, ⊕, ⊙) be as in part (a). Prove that f is one-to-one if and only if the kernel of f is {zR}.