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).

Read more about Ring Homomorphism:  Properties, Examples, Types of Ring Homomorphisms

Famous quotes containing the word ring:

    “The life of man is a self-evolving circle, which, from a ring imperceptibly small, rushes on all sides outwards to new and larger circles, and that without end.”
    —Ralph Waldo Emerson (1803–1882)