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).
Read more about Ring Homomorphism: Properties, Examples, Types of Ring Homomorphisms
Famous quotes containing the word ring:
“There is no magic decoding ring that will help us read our young adolescent’s feelings. Rather, what we need to do is hold out our antennae in the hope that we’ll pick up the right signals.”
—The Lions Clubs International and the Quest Nation. The Surprising Years, III, ch.4 (1985)