About: Algebra homomorphism

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In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if A and B are algebras over a field (or commutative ring) K, it is a function such that for all k in K and x, y in A, * * * The first two conditions say that F is a K-linear map (or K-module homomorphism if K is a commutative ring), and the last condition says that F is a (non-unital) ring homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B.

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rdf:type	yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797 yago:WikicatAlgebras
rdfs:label	Algebra homomorphism (en) Omomorfismo di algebre (it) 代數同態 (zh)
rdfs:comment	In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if A and B are algebras over a field (or commutative ring) K, it is a function such that for all k in K and x, y in A, * * * The first two conditions say that F is a K-linear map (or K-module homomorphism if K is a commutative ring), and the last condition says that F is a (non-unital) ring homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B. (en) Un omomorfismo tra due algebre sul campo K, A e B, è una funzione tale che per ogni k in K e x,y in A, * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) Se F è biettiva allora F è detta isomorfismo tra A e B. (it) 在A和B兩個K-多元環之間的同態是指一個函數，此函數能使得對所有在K內的k和在A內的x、y來說， * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) 若F是双射的，則F稱為是A和B之間的同構。 (zh)
dct:subject	Algebras Ring theory Morphisms
Wikipage page ID	331969 (xsd:integer)
Wikipage revision ID	1014718316 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebra over a field Homomorphism Algebras Ring theory Mathematics Function (mathematics) Morphism Bijective Commutative algebra Commutative ring Spectrum of a ring Morphisms Linear map Field (mathematics) Central simple algebra Isomorphism Inverse function Module homomorphism Associative algebra Augmentation (algebra) Group of units Simple algebra Overcategory Subalgebra Skolem–Noether theorem Ring homomorphism
sameAs	Algebra homomorphism Algebra homomorphism Algebra homomorphism Algebra homomorphism Algebra homomorphism Algebra homomorphism Algebra homomorphism
dbp:wikiPageUsesTemplate	dbt:Math dbt:Mvar dbt:Reflist dbt:Short_description dbt:Slink
has abstract	In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if A and B are algebras over a field (or commutative ring) K, it is a function such that for all k in K and x, y in A, * * * The first two conditions say that F is a K-linear map (or K-module homomorphism if K is a commutative ring), and the last condition says that F is a (non-unital) ring homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B. (en) Un omomorfismo tra due algebre sul campo K, A e B, è una funzione tale che per ogni k in K e x,y in A, * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) Se F è biettiva allora F è detta isomorfismo tra A e B. (it) 在A和B兩個K-多元環之間的同態是指一個函數，此函數能使得對所有在K內的k和在A內的x、y來說， * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) 若F是双射的，則F稱為是A和B之間的同構。 (zh)
prov:wasDerivedFrom	wikipedia-en:Algebra_homomorphism?oldid=1014718316&ns=0
page length (characters) of wiki page	3374 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Algebra_homomorphism
is Link from a Wikipage to another Wikipage of	Quaternion List of abstract algebra topics Ran space Representation theory Algebra representation Homomorphism Ring extension Vectorization (mathematics) Invariant subspace *-algebra Chern–Weil homomorphism Gelfand representation Clifford algebra Geometric algebra Morphism of algebraic varieties Complex affine space Zero to the power of zero Functor Prime-factor FFT algorithm Matrix ring Measuring coalgebra Ring of polynomial functions 3-sphere Exterior algebra Outermorphism Kaplansky's conjectures Universal enveloping algebra Chinese remainder theorem Symmetric algebra Weight (representation theory) Module homomorphism Augmentation (algebra) Polynomial ring Split-quaternion

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