Tor functor
In mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central concepts of homological algebra, in which ideas from algebraic topology are used to construct invariants of algebraic structures. The homology of groups, Lie algebras, and associative algebras can all be defined in terms of Tor. The name comes from a relation between the first Tor group Tor1 and the torsion subgroup of an abelian group.
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Tor functor
In mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central concepts of homological algebra, in which ideas from algebraic topology are used to construct invariants of algebraic structures. The homology of groups, Lie algebras, and associative algebras can all be defined in terms of Tor. The name comes from a relation between the first Tor group Tor1 and the torsion subgroup of an abelian group.
has abstract
Der Tor-Funktor ist ein mathem ...... nen der homologischen Algebra.
@de
En mathématiques, le foncteur ...... lation du théorème de Künneth.
@fr
En álgebra homológica, los fun ...... jo para definir el funtor Tor.
@es
In mathematics, the Tor functo ...... 1956 book Homological Algebra.
@en
Inom homologisk algebra är Tor-funktorn av tensorprodukt-funktorn.
@sv
У математиці, функтор Tor є по ...... г у книзі Homological Algebra.
@uk
ホモロジー代数において、Tor 関手 (英: Tor fun ...... テンソルして複体 を得る。そしてこの複体のホモロジーをとる。
@ja
在交換代數中,Tor 函子是張量積的導函子。此函子起初是為了表述代數拓撲中的 Künneth 定理與而定義。
@zh
호몰로지 대수학에서, Tor 함자(Tor函子, 영어: Tor functor)는 가군 텐서곱 함자의 유도 함자다.
@ko
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Der Tor-Funktor ist ein mathem ...... nen der homologischen Algebra.
@de
En mathématiques, le foncteur ...... lation du théorème de Künneth.
@fr
En álgebra homológica, los fun ...... s, LnT estarán definidos. Sea:
@es
In mathematics, the Tor functo ...... subgroup of an abelian group.
@en
Inom homologisk algebra är Tor-funktorn av tensorprodukt-funktorn.
@sv
У математиці, функтор Tor є по ...... г у книзі Homological Algebra.
@uk
ホモロジー代数において、Tor 関手 (英: Tor fun ...... テンソルして複体 を得る。そしてこの複体のホモロジーをとる。
@ja
在交換代數中,Tor 函子是張量積的導函子。此函子起初是為了表述代數拓撲中的 Künneth 定理與而定義。
@zh
호몰로지 대수학에서, Tor 함자(Tor函子, 영어: Tor functor)는 가군 텐서곱 함자의 유도 함자다.
@ko
label
Foncteur Tor
@fr
Funtor Tor
@es
Tor (Mathematik)
@de
Tor functor
@en
Tor 함자
@ko
Tor-funktorn
@sv
Tor函子
@zh
Tor関手
@ja
Функтор Tor
@uk