Topic
Torsion (algebra)
About: Torsion (algebra) is a research topic. Over the lifetime, 4992 publications have been published within this topic receiving 59895 citations.
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Book•
01 Jan 1960
TL;DR: In this paper, the authors propose a theory of homology and cohomology theories of groups and moniods, and derive derived functors from homology functors, including Tensor products, groups of homomorphisms, and projective and injective modules.
Abstract: Preface 1. Generalities concerning modules 2. Tensor products and groups of homomorphisms 3. Categories and functors 4. Homology functors 5. Projective and injective modules 6. Derived functors 7. Torsion and extension functors 8. Some useful identities 9. Commutative Noetherian rings of finite global dimension 10. Homology and cohomology theories of groups and moniods Notes References Index.
2,253 citations
Book•
[...]
01 Jan 1969
TL;DR: The notions of torsion and freeness have played a very important role in module theory as discussed by the authors, particularly in the study of modules over integral domains, and the use of homological techniques in this connection has been well established.
Abstract: The notions of torsion and torsion freeness have played a very important role in module theory--particularly in the study of modules over integral domains. Furthermore, the use of homological techniques in this connection has been well established. It is the aim of this paper to extend these techniques and to show that this extension leads naturally to several new concepts (e.g. k-torsion freeness and Gorenstein dimension) which are useful in the classification of modules and rings.
1,161 citations
TL;DR: An analogue of projective scheme is defined for noncommutative N-graded algebras using the quotient category C of graded right A-modules modulo its full subcategory of torsion modules.
616 citations
508 citations
Book•
22 Jul 2007
TL;DR: Torsion pairs in abelian and triangulated categories Torsion pair in pretriangulated classes Compactly generated torsions in triangulation categories Hereditary torsion paired in triagonality categories TORSion pairs and closed model structures (Co)torsions and generalized Tate-Vogel cohomology Nakayama categories and Cohen-Macaulay cohology Bibliography Index as mentioned in this paper.
Abstract: Introduction Torsion pairs in abelian and triangulated categories Torsion pairs in pretriangulated categories Compactly generated torsion pairs in triangulated categories Hereditary torsion pairs in triangulated categories Torsion pairs in stable categories Triangulated torsion(-free) classes in stable categories Gorenstein categories and (co)torsion pairs Torsion pairs and closed model structures (Co)torsion pairs and generalized Tate-Vogel cohomology Nakayama categories and Cohen-Macaulay cohomology Bibliography Index.
447 citations