Ring

Ring homomorphism

A ring homomorphism is a structure-preserving map between rings. #m/def/ring Let be rings and let . Then is a ring homomorphism iff is a rng homomorphism and in addition

Sometimes these are referred to as unital ring homomorphisms. These are the morphisms in .

Properties

• A ring homomorphism is monic iff it is injective iff
• A ring epimorphism need not be surjective
  • e.g. inclusion . If and agree on they agree everywhere.

#state/tidy | #lang/en | #SemBr