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:
“This is the gospel of labour, ring it, ye bells of the kirk!
The Lord of Love came down from above, to live with the men who work.
This is the rose that He planted, here in the thorn-curst soil:
Heaven is blest with perfect rest, but the blessing of Earth is toil.”
—Henry Van Dyke (1852–1933)