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natural homomorphism
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(Definition)
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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.
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"natural homomorphism" is owned by iwnbap.
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Cross-references: groups, homomorphism, operations, coset, map, ideal, ring
There are 8 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 6373 times total.
Classification:
| AMS MSC: | 13B10 (Commutative rings and algebras :: Ring extensions and related topics :: Morphisms) |
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Pending Errata and Addenda
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