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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 wikiPageLength "9681".
- Ring_homomorphism wikiPageOutDegree "54".
- Ring_homomorphism wikiPageRevisionID "706841446".
- Ring_homomorphism wikiPageWikiLink Abstract_algebra.
- Ring_homomorphism wikiPageWikiLink Bijection.
- Ring_homomorphism wikiPageWikiLink Category:Morphisms.
- Ring_homomorphism wikiPageWikiLink Category:Ring_theory.
- Ring_homomorphism wikiPageWikiLink Category_(mathematics).
- Ring_homomorphism wikiPageWikiLink Category_of_rings.
- Ring_homomorphism wikiPageWikiLink Change_of_rings.
- Ring_homomorphism wikiPageWikiLink Characteristic_(algebra).
- Ring_homomorphism wikiPageWikiLink Class_(set_theory).
- Ring_homomorphism wikiPageWikiLink Complex_conjugate.
- Ring_homomorphism wikiPageWikiLink Complex_number.
- Ring_homomorphism wikiPageWikiLink David_Eisenbud.
- Ring_homomorphism wikiPageWikiLink Divisor.
- Ring_homomorphism wikiPageWikiLink Epimorphism.
- Ring_homomorphism wikiPageWikiLink Field_(mathematics).
- Ring_homomorphism wikiPageWikiLink Field_extension.
- Ring_homomorphism wikiPageWikiLink Function_(mathematics).
- Ring_homomorphism wikiPageWikiLink Function_composition.
- Ring_homomorphism wikiPageWikiLink Group_homomorphism.
- Ring_homomorphism wikiPageWikiLink Ian_G._Macdonald.
- Ring_homomorphism wikiPageWikiLink Ideal_(ring_theory).
- Ring_homomorphism wikiPageWikiLink Image_(mathematics).
- Ring_homomorphism wikiPageWikiLink Initial_and_terminal_objects.
- Ring_homomorphism wikiPageWikiLink Integral_domain.
- Ring_homomorphism wikiPageWikiLink Isomorphism.
- Ring_homomorphism wikiPageWikiLink Kernel_(algebra).
- Ring_homomorphism wikiPageWikiLink Matrix_ring.
- Ring_homomorphism wikiPageWikiLink Maximal_ideal.
- Ring_homomorphism wikiPageWikiLink Michael_Artin.
- Ring_homomorphism wikiPageWikiLink Michael_Atiyah.
- Ring_homomorphism wikiPageWikiLink Michiel_Hazewinkel.
- Ring_homomorphism wikiPageWikiLink Modular_arithmetic.
- Ring_homomorphism wikiPageWikiLink Monomorphism.
- Ring_homomorphism wikiPageWikiLink Morphism.
- Ring_homomorphism wikiPageWikiLink Nathan_Jacobson.
- Ring_homomorphism wikiPageWikiLink Nicolas_Bourbaki.
- Ring_homomorphism wikiPageWikiLink Polynomial.
- Ring_homomorphism wikiPageWikiLink Prime_ideal.
- Ring_homomorphism wikiPageWikiLink Real_number.
- Ring_homomorphism wikiPageWikiLink Ring_(mathematics).
- Ring_homomorphism wikiPageWikiLink Ring_theory.
- Ring_homomorphism wikiPageWikiLink Rng_(algebra).
- Ring_homomorphism wikiPageWikiLink Serge_Lang.
- Ring_homomorphism wikiPageWikiLink Strong_epimorphism.
- Ring_homomorphism wikiPageWikiLink Subring.
- Ring_homomorphism wikiPageWikiLink Surjective_function.
- Ring_homomorphism wikiPageWikiLink Zero_ring.
- Ring_homomorphism wikiPageWikiLinkText "Ring homomorphism".
- Ring_homomorphism wikiPageWikiLinkText "field homomorphism".
- Ring_homomorphism wikiPageWikiLinkText "homomorphic".
- Ring_homomorphism wikiPageWikiLinkText "homomorphism of rings".
- Ring_homomorphism wikiPageWikiLinkText "homomorphism".
- Ring_homomorphism wikiPageWikiLinkText "isomorphic".
- Ring_homomorphism wikiPageWikiLinkText "isomorphism".
- Ring_homomorphism wikiPageWikiLinkText "ring automorphism".
- Ring_homomorphism wikiPageWikiLinkText "ring homomorphism".
- Ring_homomorphism wikiPageWikiLinkText "ring homomorphism#Endomorphisms, isomorphisms, and automorphisms".
- Ring_homomorphism wikiPageUsesTemplate Template:Main.
- Ring_homomorphism subject Category:Morphisms.
- Ring_homomorphism subject Category:Ring_theory.
- Ring_homomorphism hypernym Function.
- Ring_homomorphism type Disease.
- Ring_homomorphism type Function.
- Ring_homomorphism type Morphism.
- Ring_homomorphism type Redirect.
- Ring_homomorphism comment "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. ".
- Ring_homomorphism label "Ring homomorphism".
- Ring_homomorphism sameAs Q1194212.
- Ring_homomorphism sameAs Okruhový_homomorfismus.
- Ring_homomorphism sameAs Ringhomomorphismus.
- Ring_homomorphism sameAs Ομομορφισμός_δακτυλίων.
- Ring_homomorphism sameAs Homomorfismo_de_anillos.
- Ring_homomorphism sameAs Morphisme_danneaux.
- Ring_homomorphism sameAs Omomorfismo_di_anelli.
- Ring_homomorphism sameAs 環準同型.
- Ring_homomorphism sameAs 환_준동형사상.
- Ring_homomorphism sameAs Ringhomomorfisme.
- Ring_homomorphism sameAs ਰਿੰਗ_ਹੋਮੋਮੌਰਫਿਜ਼ਮ.
- Ring_homomorphism sameAs Homomorfizm_pierścieni.
- Ring_homomorphism sameAs Homomorfismo_de_anéis.
- Ring_homomorphism sameAs m.06l1p.
- Ring_homomorphism sameAs Q1194212.
- Ring_homomorphism sameAs 环同态.
- Ring_homomorphism wasDerivedFrom Ring_homomorphism?oldid=706841446.
- Ring_homomorphism isPrimaryTopicOf Ring_homomorphism.