Edgar E. Enochs, Overtoun M. G. Jenda

Relative Homological Algebra (eBook, PDF)

• Format: PDF

Produktbeschreibung

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, 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 interested in a thorough study of the subject.

Editorial Board

Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Aix-Marseille Université, France
Katrin Wendland, Trinity College Dublin, Dublin, Ireland

Honorary Editor

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

Titles in planning include

Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, BoStjan GabrovSek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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Produktdetails

• Verlag: Walter de Gruyter
• Seitenzahl: 350
• Erscheinungstermin: 20. April 2011
• Englisch
• ISBN-13: 9783110803662
• Artikelnr.: 35697389

Autorenporträt

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

Inhaltsangabe

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

Rezensionen

"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

"As their book is primarily aimed at graduate students in homological algebra, the authors have made any effort to keep the text reasonably self-contained and detailed. The outcome is a comprehensive textbook on relative homological algebra at its present state of art." Zentralblatt für Mathematik (review of the first edition)

"[...] in the reviewer's opinion it is an elegant introduction to homological methods towards applications in ring theory." Zentralblatt für Mathematik