Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Weak_dimension> ?p ?o. }
Showing items 1 to 21 of
21
with 100 items per page.
- Weak_dimension abstract "In abstract algebra, the weak dimension of a nonzero right module M over a ring R is the largest number n such that the Tor group TorRn(M,N) is nonzero for some left R-module N (or infinity if no largest such n exists), and the weak dimension of a left R-module is defined similarly. The weak dimension was introduced by Cartan and Eilenberg (1956, p.122). The weak dimension is sometimes called the flat dimension as it is the shortest length of a resolution of the module by flat modules. The weak dimension a module is at most equal to its projective dimension.The weak global dimension of a ring is the largest number n such that TorRn(M,N) is nonzero for some right R-module M and left R-module N. If there is no such largest number n, the weak global dimension is defined to be infinite. It is at most equal to the left or right global dimension of the ring R.".
- Weak_dimension wikiPageExternalLink books?id=0268b52ghcsC.
- Weak_dimension wikiPageID "38263686".
- Weak_dimension wikiPageRevisionID "543093685".
- Weak_dimension b "n".
- Weak_dimension hasPhotoCollection Weak_dimension.
- Weak_dimension last "Cartan".
- Weak_dimension last "Eilenberg".
- Weak_dimension loc "p.122".
- Weak_dimension p "R".
- Weak_dimension year "1956".
- Weak_dimension subject Category:Commutative_algebra.
- Weak_dimension subject Category:Homological_algebra.
- Weak_dimension subject Category:Ring_theory.
- Weak_dimension comment "In abstract algebra, the weak dimension of a nonzero right module M over a ring R is the largest number n such that the Tor group TorRn(M,N) is nonzero for some left R-module N (or infinity if no largest such n exists), and the weak dimension of a left R-module is defined similarly. The weak dimension was introduced by Cartan and Eilenberg (1956, p.122). The weak dimension is sometimes called the flat dimension as it is the shortest length of a resolution of the module by flat modules.".
- Weak_dimension label "Weak dimension".
- Weak_dimension sameAs m.0py154z.
- Weak_dimension sameAs Q17104628.
- Weak_dimension sameAs Q17104628.
- Weak_dimension wasDerivedFrom Weak_dimension?oldid=543093685.
- Weak_dimension isPrimaryTopicOf Weak_dimension.