Ring Homomorphism

In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication.

More precisely, if R and S are rings, then a ring homomorphism is a function f : R → S such that

• f(a + b) = f(a) + f(b) for all a and b in R
• f(ab) = f(a) f(b) for all a and b in R

The composition of two ring homomorphisms is a ring homomorphism. It follows that the class of all rings forms a category with ring homomorphisms as the morphisms (cf. the category of rings).