natural homomorphism

The natural homomorphism $R\to R/I$ 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
Canonical name	NaturalHomomorphism
Date of creation	2013-03-22 14:33:32
Last modified on	2013-03-22 14:33:32
Owner	iwnbap (1760)
Last modified by	iwnbap (1760)
Numerical id	8
Author	iwnbap (1760)
Entry type	Definition
Classification	msc 13B10
Related topic	Homomorphism
Related topic	QuotientRing
Defines	Natural homomorphism