Relative Homological Algebra

Inbunden, Engelska, 2011

Av Edgar E. Enochs, Overtoun M. G. Jenda

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This second volume deals with the relative homological algebra of complexes of modules and their applications. It is a concrete and easy introduction to the kind of homological algebra which has been developed in the last 50 years. The book serves as a bridge between the traditional texts on homological algebra and more advanced topics such as triangulated and derived categories or model category structures. It addresses to readers who have had a course in classical homological algebra, as well as to researchers.

Produktinformation

Utgivningsdatum2011-08-18
Mått170 x 240 x 12 mm
Vikt331 g
FormatInbunden
SpråkEngelska
SerieDe Gruyter Expositions in Mathematics
Antal sidor108
Upplaga11001
FörlagDe Gruyter
ISBN9783110215229

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Algebra inom Naturvetenskap och teknik

DedicationPrefaceChapter I: Complexes of Modules1. Definitions and basic constructions2. Complexes formed from Modules3. Free Complexes4. Projective and Injective ComplexesChapter II: Short Exact Sequences of Complexe1. The groups Extn(C, D)2. The Group Ext1(C, D)3. The Snake Lemma for Complexes4. Mapping ConesChapter III: The Category K(R-Mod)1. Homotopies2. The category K(R-Mod)3. Split short exact sequences4. The complexes Hom(C, D)5. The Koszul ComplexChapter IV: Cotorsion Pairs and Triplets in C(R-Mod)1. Cotorsion Pairs2. Cotorsion triplets3. The Dold triplet4. More on cotorsion pairs and tripletsChapter V: Adjoint Functors1. Adjoint functorsChapter VI: Model Structures1. Model Structures on C(R-Mod)Chapter VII: Creating Cotorsion Pairs1. Creating Cotorsion pairs in C(R-Mod) in a Termwise Manner2. The Hill lemma3. More cotorsion pairs4. More Hovey pairsChapter VIII: Minimal Complexes1. Minimal resolutions2. Decomposing a complexChapter IX: Cartan and Eilenberg Resolutions1. Cartan-Eilenberg Projective Complexes2. Cartan and Eilenberg Projective resolutions3. C - E injective complexes and resolutions4. Cartan and Eilenberg BalanceBibliographical NotesReferencesIndex