# natural homomorphism

The natural homomorphism $R\rightarrow R/I$ where $R$ is a ring and $I$ an ideal of $R$ is the map $\alpha\mapsto\alpha+I$. Coset operations, e.g $(\alpha+\beta)+I=(\alpha+I)+(\beta+I)$ guarantee this will be a homomorphism. Natural homomorphisms for groups can be defined similarly.

Title natural homomorphism NaturalHomomorphism 2013-03-22 14:33:32 2013-03-22 14:33:32 iwnbap (1760) iwnbap (1760) 8 iwnbap (1760) Definition msc 13B10 Homomorphism QuotientRing Natural homomorphism