About: Graded vector space

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In mathematics, a graded vector space is a vector space that has the extra structure of a grading or a gradation, which is a decomposition of the vector space into a direct sum of vector subspaces.

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rdf:type	yago:WikicatCategory-theoreticCategories yago:WikicatVectorSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:Class107997703 yago:Collection107951464 yago:Group100031264 yago:Space100028651
rdfs:label	Espace gradué (fr) Graded vector space (en) 次数付きベクトル空間 (ja) 등급 가군 (ko)
rdfs:comment	In mathematics, a graded vector space is a vector space that has the extra structure of a grading or a gradation, which is a decomposition of the vector space into a direct sum of vector subspaces. (en) 환론에서 등급 가군(等級加群, 영어: graded module)은 등급이 붙어, 등급환이 (왼쪽 또는 오른쪽에서) 작용할 수 있는 가군이다. (ko) 数学における次数付きベクトル空間（じすうつきベクトルくうかん、英: graded vector space; 次数ベクトル空間、次数付き線型空間、次数線型空間）は、 (grading) と呼ばれる追加の構造を持つベクトル空間であり、次数付けにより適当な線型部分空間の直和として記述される。 (ja) En mathématiques, un espace gradué est un espace vectoriel ou plus généralement un groupe abélien muni d'une décomposition en somme directe de sous-espaces, indexée par un ensemble d'entiers (naturels ou relatifs) ou par un groupe cyclique. Une graduation est la donnée d'une telle décomposition. Une graduation facilite souvent les calculs, notamment en algèbre homologique, en ne travaillant qu'avec des éléments homogènes en chaque degré, ce qui permet par exemple de se ramener dans bien des cas à des espaces de dimension finie. (fr)
dcterms:subject	Vector spaces Categories in category theory
Wikipage page ID	1155734 (xsd:integer)
Wikipage revision ID	1110774388 (xsd:integer)
Link from a Wikipage to another Wikipage	Monomial Vector spaces Vector space Degree of a polynomial Commutative monoid Mathematics Graded (mathematics) Graded algebra Graded module Monoid Morphism Littlewood–Richardson rule Comodule Embedding Physics Linear map Linear subspace Semigroup Field (mathematics) Formal power series Nicolas Bourbaki Hilbert–Poincaré series Ring (mathematics) Abelian group Associative algebra Categories in category theory Polynomial Endomorphism algebra Integer Natural number Cancellation property Category (mathematics) Direct sum of vector spaces Supervector space
sameAs	Graded vector space Graded vector space Graded vector space Graded vector space Graded vector space Graded vector space Graded vector space Graded vector space
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:ISBN dbt:Math dbt:Short_description dbt:Use_American_English
has abstract	In mathematics, a graded vector space is a vector space that has the extra structure of a grading or a gradation, which is a decomposition of the vector space into a direct sum of vector subspaces. (en) En mathématiques, un espace gradué est un espace vectoriel ou plus généralement un groupe abélien muni d'une décomposition en somme directe de sous-espaces, indexée par un ensemble d'entiers (naturels ou relatifs) ou par un groupe cyclique. Une graduation est la donnée d'une telle décomposition. Une graduation facilite souvent les calculs, notamment en algèbre homologique, en ne travaillant qu'avec des éléments homogènes en chaque degré, ce qui permet par exemple de se ramener dans bien des cas à des espaces de dimension finie. Le gradué associé à une filtration est l'espace obtenu comme somme des quotients de termes consécutifs. La graduation peut être compatible avec d'autres structures, comme la multiplication dans une algèbre graduée, ou la différentielle dans un complexe de chaines. (fr) 환론에서 등급 가군(等級加群, 영어: graded module)은 등급이 붙어, 등급환이 (왼쪽 또는 오른쪽에서) 작용할 수 있는 가군이다. (ko) 数学における次数付きベクトル空間（じすうつきベクトルくうかん、英: graded vector space; 次数ベクトル空間、次数付き線型空間、次数線型空間）は、 (grading) と呼ばれる追加の構造を持つベクトル空間であり、次数付けにより適当な線型部分空間の直和として記述される。 (ja)
gold:hypernym	Space
prov:wasDerivedFrom	wikipedia-en:Graded_vector_space?oldid=1110774388&ns=0
page length (characters) of wiki page	5617 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Graded_vector_space
is Link from a Wikipage to another Wikipage of	Anyonic Lie algebra Vector (mathematics and physics) Vector space Lie algebra representation Cross product Geometric algebra Graded (mathematics) Monstrous moonshine Super vector space Comodule Frölicher–Nijenhuis bracket Category of graded vector spaces Differential graded Lie algebra Graded Lie algebra Graded ring Hilbert series and Hilbert polynomial Hilbert–Poincaré series Khovanov homology Grade Resolution (algebra) BRST quantization Supersymmetric gauge theory Symmetric algebra Symmetry in mathematics Homotopy Lie algebra

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