Ring Homomorphisms

Abstract

• If R and S are ring, a function f : R → S is a ring homomorphism (or a ring map) if f (x + y) = f (x) + f (y) and f (xy) = f (x)f (y) for all x, y ∈ R. If R and S are rings with identity, it's customary to also require that f (1) = 1.