About: Nilpotent algebra

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In mathematics, specifically in ring theory, a nilpotent algebra over a commutative ring is an algebra over a commutative ring, in which for some positive integer n every product containing at least n elements of the algebra is zero. The concept of a nilpotent Lie algebra has a different definition, which depends upon the Lie bracket. (There is no Lie bracket for many algebras over commutative rings; a Lie algebra involves its Lie bracket, whereas, there is no Lie bracket defined in the general case of an algebra over a commutative ring.) Another possible source of confusion in terminology is the quantum nilpotent algebra, a concept related to quantum groups and Hopf algebras.

Attributes	Values
rdfs:label	Algèbre nilpotente (fr) Nilpotent algebra (en)
rdfs:comment	In mathematics, specifically in ring theory, a nilpotent algebra over a commutative ring is an algebra over a commutative ring, in which for some positive integer n every product containing at least n elements of the algebra is zero. The concept of a nilpotent Lie algebra has a different definition, which depends upon the Lie bracket. (There is no Lie bracket for many algebras over commutative rings; a Lie algebra involves its Lie bracket, whereas, there is no Lie bracket defined in the general case of an algebra over a commutative ring.) Another possible source of confusion in terminology is the quantum nilpotent algebra, a concept related to quantum groups and Hopf algebras. (en) En mathématiques, une algèbre nilpotente est une algèbre associative sans unité pour laquelle tous les produits sont nuls à partir d’un certain nombre de facteurs. Cette propriété se traduit par l’identité polynomiale x1x2…xn = 0 et implique en particulier que tous les éléments de l’algèbre sont nilpotents, mais la réciproque est fausse. La plus petite valeur de n pour laquelle l’identité est satisfaite est l’ordre de nilpotence de l’algèbre. La définition s’étend au cas des par l’annulation de tous les produits de n termes quel que soit le . * Portail de l’algèbre (fr)
dcterms:subject	Algebras Ring theory Properties of binary operations
Wikipage page ID	42046875 (xsd:integer)
Wikipage revision ID	1019250811 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebra (ring theory) Algebraic structure Algebras Ring theory Mathematics Nilpotent Lie algebra Hopf algebra Nil-Coxeter algebra Properties of binary operations Nilpotent Lie algebra Non-associative algebra Ring theory Associativity Associative algebra Example of a non-associative algebra Quantum group Power associative Lie bracket
Link from a Wikipage to an external page	http://www.encyclopediaofmath.org/index.php/Nilpotent_algebra
sameAs	Nilpotent algebra Nilpotent algebra Nilpotent algebra Nilpotent algebra
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Lang_Algebra
has abstract	In mathematics, specifically in ring theory, a nilpotent algebra over a commutative ring is an algebra over a commutative ring, in which for some positive integer n every product containing at least n elements of the algebra is zero. The concept of a nilpotent Lie algebra has a different definition, which depends upon the Lie bracket. (There is no Lie bracket for many algebras over commutative rings; a Lie algebra involves its Lie bracket, whereas, there is no Lie bracket defined in the general case of an algebra over a commutative ring.) Another possible source of confusion in terminology is the quantum nilpotent algebra, a concept related to quantum groups and Hopf algebras. (en) En mathématiques, une algèbre nilpotente est une algèbre associative sans unité pour laquelle tous les produits sont nuls à partir d’un certain nombre de facteurs. Cette propriété se traduit par l’identité polynomiale x1x2…xn = 0 et implique en particulier que tous les éléments de l’algèbre sont nilpotents, mais la réciproque est fausse. La plus petite valeur de n pour laquelle l’identité est satisfaite est l’ordre de nilpotence de l’algèbre. La définition s’étend au cas des par l’annulation de tous les produits de n termes quel que soit le . En particulier, tout idéal d’une algèbre constitue une algèbre nilpotente. Si R est un anneau commutatif, l’ensemble des matrices triangulaires supérieures strictes de forme une algèbre nilpotente d’ordre n. * Portail de l’algèbre (fr)
prov:wasDerivedFrom	wikipedia-en:Nilpotent_algebra?oldid=1019250811&ns=0
page length (characters) of wiki page	2802 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Nilpotent_algebra
is Link from a Wikipage to another Wikipage of	Nil algebra Non-associative algebra Nilpotent algebra (ring theory) Nilalgebra
is Wikipage redirect of	Nil algebra Nilpotent algebra (ring theory) Nilalgebra
is foaf:primaryTopic of	wikipedia-en:Nilpotent_algebra

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