Relative Homological Algebra

ISBN-13: 9783110215229 / Angielski / Twarda / 2011 / 108 str.

Opis

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.

Recenzje

"The authors' presentation is original, condensed and carefully written. Even in case the authors' would be right with their claim that the results "are probably well known" it will be an important help for a person who will become familiar with these details to find them in such a compact and clearly presented way." Zentralblatt für Mathematik

Spis treści

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

O autorze

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