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In mathematics, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function f : R → S that preserves addition, multiplication and multiplicative identity; that is,
Properties, Examples & Category of rings
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ring homomorphism rings category function isomorphism ideal zero isomorphic also homomorphisms kernel surjective every identity rng see map defined two
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Ring homomorphism | is a | structure-preserving function between two rings | 0.90 | text |
| Ring homomorphism | is a | function f | 0.90 | text |
| Ring homomorphism | is a | isomorphism if and only if it is bijective as a function on the underlying sets | 0.90 | text |
| Ring homomorphism | related to Endomorphisms, isomorphisms, and automorphisms | One | 0.60 | section |
| Ring homomorphism | related to Endomorphisms, isomorphisms, and automorphisms | If | 0.60 | section |
| Ring homomorphism | related to Endomorphisms, isomorphisms, and automorphisms | Isomorphic | 0.60 | section |
| Ring homomorphism | related to Endomorphisms, isomorphisms, and automorphisms | Example | 0.60 | section |
| Ring homomorphism | related to Endomorphisms, isomorphisms, and automorphisms | Up | 0.60 | section |
| Ring homomorphism | related to Endomorphisms, isomorphisms, and automorphisms | This | 0.60 | section |
| Ring homomorphism | related to Endomorphisms, isomorphisms, and automorphisms | On | 0.60 | section |
| Ring homomorphism | related to Examples | The | 0.60 | section |
| Ring homomorphism | related to Examples | Z/nZ | 0.60 | section |
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