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Relative Homological Algebra de Edgar E. Enochs

Relative Homological Algebra: De Gruyter Expositions in Mathematics, cartea 30

Autor Edgar E. Enochs, Overtoun M. G. Jenda
en Limba Engleză Hardback – 21 mar 2000

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.

Editorial Board

Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Walter D. Neumann, Columbia University, New York, USA

Markus J. Pflaum, University of Colorado, Boulder, USA

Dierk Schleicher, Jacobs University, Bremen, Germany"

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Specificații

ISBN-13: 9783110166330
ISBN-10: 311016633X
Pagini: 350
Dimensiuni: 155 x 230 x 29 mm
Greutate: 0.72 kg
Ediția:Reprint 2011
Editura: De Gruyter
Colecția De Gruyter
Seria De Gruyter Expositions in Mathematics

Locul publicării:Berlin/Boston

Notă biografică

Edgar E. Enochs, University of Kentucky, Lexington, USA; Overtoun M. G. Jenda, Auburn University, Alabama, USA.

Cuprins

AD>Dedication Preface
Chapter I: Complexes of Modules 1. Definitions and basic constructions 2. Complexes formed from Modules 3. Free Complexes 4. Projective and Injective Complexes
Chapter II: Short Exact Sequences of Complexe 1. The groups Extn(C, D) 2. The Group Ext1(C, D) 3. The Snake Lemma for Complexes 4. Mapping Cones
Chapter III: The Category K(R-Mod) 1. Homotopies 2. The category K(R-Mod) 3. Split short exact sequences 4. The complexes Hom(C, D) 5. The Koszul Complex
Chapter IV: Cotorsion Pairs and Triplets in C(R-Mod) 1. Cotorsion Pairs 2. Cotorsion triplets 3. The Dold triplet 4. More on cotorsion pairs and triplets
Chapter V: Adjoint Functors 1. Adjoint functors
Chapter VI: Model Structures 1. Model Structures on C(R-Mod)
Chapter VII: Creating Cotorsion Pairs 1. Creating Cotorsion pairs in C(R-Mod) in a Termwise Manner 2. The Hill lemma 3. More cotorsion pairs 4. More Hovey pairs
Chapter VIII: Minimal Complexes 1. Minimal resolutions 2. Decomposing a complex
Chapter IX: Cartan and Eilenberg Resolutions 1. Cartan-Eilenberg Projective Complexes 2. Cartan and Eilenberg Projective resolutions 3. C - E injective complexes and resolutions 4. Cartan and Eilenberg Balance
Bibliographical Notes References Index