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natural homomorphism (Definition)

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.



"natural homomorphism" is owned by iwnbap.
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See Also: homomorphism, quotient ring

Also defines:  Natural homomorphism
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Cross-references: groups, homomorphism, operations, coset, map, ideal, ring
There are 6 references to this entry.

This is version 5 of natural homomorphism, born on 2004-08-24, modified 2004-08-25.
Object id is 6112, canonical name is NaturalHomomorphism.
Accessed 5187 times total.

Classification:
AMS MSC: 13B10 (Commutative rings and algebras :: Ring extensions and related topics :: Morphisms)
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