| http://dbpedia.org/ontology/abstract
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In mathematics, an exp algebra is a Hopf a … In mathematics, an exp algebra is a Hopf algebra Exp(G) constructed from an abelian group G, and is the universal ring R such that there is an exponential map from G to the group of the power series in R[[t]] with constant term 1. In other words the functor Exp from abelian groups to commutative rings is adjoint to the functor from commutative rings to abelian groups taking a ring to the group of formal power series with constant term 1. The definition of the exp ring of G is similar to that of the group ring Z[G] of G, which is the universal ring such that there is an exponential homomorphism from the group to its units. In particular there is a natural homomorphism from the group ring to a completion of the exp ring. However in general the Exp ring can be much larger than the group ring: for example, the group ring of the integers is the ring of Laurent polynomials in 1 variable, while the exp ring is a polynomial ring in countably many generators.ynomial ring in countably many generators.
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3506
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1115805271
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, http://dbpedia.org/resource/Universal_property +
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| http://dbpedia.org/property/first
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V. V.
, Michiel
, Nadiya
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| http://dbpedia.org/property/isbn
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978
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| http://dbpedia.org/property/last
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Gubareni
, Hazewinkel
, Kirichenko
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| http://dbpedia.org/property/mr
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2724822
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| http://dbpedia.org/property/place
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Providence, RI
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| http://dbpedia.org/property/publisher
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American Mathematical Society
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| http://dbpedia.org/property/series
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Mathematical Surveys and Monographs
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| http://dbpedia.org/property/title
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Algebras, rings and modules.
Lie algebras and Hopf algebras
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| http://dbpedia.org/property/volume
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168
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| http://dbpedia.org/property/year
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2010
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| http://dbpedia.org/property/zbl
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1211.16023
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| http://purl.org/dc/terms/subject
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http://dbpedia.org/resource/Category:Hopf_algebras +
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http://dbpedia.org/resource/Exp +
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| rdfs:comment |
In mathematics, an exp algebra is a Hopf a … In mathematics, an exp algebra is a Hopf algebra Exp(G) constructed from an abelian group G, and is the universal ring R such that there is an exponential map from G to the group of the power series in R[[t]] with constant term 1. In other words the functor Exp from abelian groups to commutative rings is adjoint to the functor from commutative rings to abelian groups taking a ring to the group of formal power series with constant term 1. formal power series with constant term 1.
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| rdfs:label |
Exp algebra
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