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- Tor_functor abstract "In homological algebra, the Tor functors are the derived functors of the tensor product functor. They were first defined in generality to express the Künneth theorem and universal coefficient theorem in algebraic topology.[citation needed]Specifically, suppose R is a ring, and denote by R-Mod the category of left R-modules and by Mod-R the category of right R-modules (if R is commutative, the two categories coincide). Pick a fixed module B in R-Mod. For A in Mod-R, set T(A) = A⊗RB. Then T is a right exact functor from Mod-R to the category of abelian groups Ab (in the case when R is commutative, it is a right exact functor from Mod-R to Mod-R) and its left derived functors LnT are defined. We set i.e., we take a projective resolution then remove the A term and tensor the projective resolution with B to get the complex (note that A⊗RB does not appear and the last arrow is just the zero map) and take the homology of this complex.".
- Tor_functor wikiPageID "856347".
- Tor_functor wikiPageRevisionID "594382749".
- Tor_functor b "1".
- Tor_functor b "n".
- Tor_functor hasPhotoCollection Tor_functor.
- Tor_functor p "R".
- Tor_functor p "Z".
- Tor_functor subject Category:Binary_operations.
- Tor_functor subject Category:Homological_algebra.
- Tor_functor type BinaryOperations.
- Tor_functor type BooleanOperation113440935.
- Tor_functor type DataProcessing113455487.
- Tor_functor type Operation113524925.
- Tor_functor type PhysicalEntity100001930.
- Tor_functor type Process100029677.
- Tor_functor type Processing113541167.
- Tor_functor comment "In homological algebra, the Tor functors are the derived functors of the tensor product functor. They were first defined in generality to express the Künneth theorem and universal coefficient theorem in algebraic topology.[citation needed]Specifically, suppose R is a ring, and denote by R-Mod the category of left R-modules and by Mod-R the category of right R-modules (if R is commutative, the two categories coincide). Pick a fixed module B in R-Mod. For A in Mod-R, set T(A) = A⊗RB.".
- Tor_functor label "Foncteur Tor".
- Tor_functor label "Tor (Mathematik)".
- Tor_functor label "Tor functor".
- Tor_functor label "Tor函子".
- Tor_functor sameAs Tor_(Mathematik).
- Tor_functor sameAs Foncteur_Tor.
- Tor_functor sameAs Tor_함자.
- Tor_functor sameAs m.03hp6m.
- Tor_functor sameAs Q988381.
- Tor_functor sameAs Q988381.
- Tor_functor sameAs Tor_functor.
- Tor_functor wasDerivedFrom Tor_functor?oldid=594382749.
- Tor_functor isPrimaryTopicOf Tor_functor.