Edgar E. Enochs, Overtoun M. G. Jenda

Relative Homological Algebra (eBook, PDF)

Volume 1

• Format: PDF

Produktbeschreibung

This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists.

In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following:

• Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3.
• Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader.
• Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published.

The authors also have clarified some text throughout the book and updated the bibliography by adding new references.

The book is also suitable for an introductory course in commutative and ordinary homological algebra.

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Produktdetails

• Verlag: De Gruyter
• Seitenzahl: 372
• Erscheinungstermin: 27. Oktober 2011
• Englisch
• ISBN-13: 9783110215212
• Artikelnr.: 48600070

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