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- Ring_homomorphism abstract "In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure. More explicitly, if R and S are rings, then a ring homomorphism is a function f : R → S such that f(a + b) = f(a) + f(b) for all a and b in R f(ab) = f(a) f(b) for all a and b in R f(1R) = 1S.(Additive inverses and the additive identity are part of the structure too, but it is not necessary to require explicitly that they too are respected, because these conditions are consequences of the three conditions above. On the other hand, neglecting to include the condition f(1R) = 1S would cause several of the properties below to fail.)If R and S are rngs (also known as pseudo-rings, or non-unital rings), then the natural notion is that of a rng homomorphism, defined as above except without the third condition f(1R) = 1S. It is possible to have a rng homomorphism between (unital) rings that is not a ring homomorphism.The composition of two ring homomorphisms is a ring homomorphism. It follows that the class of all rings forms a category with ring homomorphisms as the morphisms (cf. the category of rings).In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.".
- Ring_homomorphism wikiPageID "26411".
- Ring_homomorphism wikiPageRevisionID "602915557".
- Ring_homomorphism hasPhotoCollection Ring_homomorphism.
- Ring_homomorphism subject Category:Morphisms.
- Ring_homomorphism subject Category:Ring_theory.
- Ring_homomorphism comment "In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.".
- Ring_homomorphism label "Homomorfismo de anillos".
- Ring_homomorphism label "Homomorfismo de anéis".
- Ring_homomorphism label "Homomorfizm pierścieni".
- Ring_homomorphism label "Morphisme d'anneaux".
- Ring_homomorphism label "Omomorfismo di anelli".
- Ring_homomorphism label "Ring homomorphism".
- Ring_homomorphism label "Ringhomomorfisme".
- Ring_homomorphism label "Ringhomomorphismus".
- Ring_homomorphism label "环同态".
- Ring_homomorphism sameAs Okruhový_homomorfismus.
- Ring_homomorphism sameAs Ringhomomorphismus.
- Ring_homomorphism sameAs Ομομορφισμός_δακτυλίων.
- Ring_homomorphism sameAs Homomorfismo_de_anillos.
- Ring_homomorphism sameAs Morphisme_d'anneaux.
- Ring_homomorphism sameAs Omomorfismo_di_anelli.
- Ring_homomorphism sameAs 환_준동형사상.
- Ring_homomorphism sameAs Ringhomomorfisme.
- Ring_homomorphism sameAs Homomorfizm_pierścieni.
- Ring_homomorphism sameAs Homomorfismo_de_anéis.
- Ring_homomorphism sameAs m.06l1p.
- Ring_homomorphism sameAs Q1194212.
- Ring_homomorphism sameAs Q1194212.
- Ring_homomorphism wasDerivedFrom Ring_homomorphism?oldid=602915557.
- Ring_homomorphism isPrimaryTopicOf Ring_homomorphism.