natural homomorphism
The natural homomorphism
R→R/I where R is a ring and I an ideal of R is the map α↦α+I. Coset operations
, e.g (α+β)+I=(α+I)+(β+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 |