Relative Homological Algebra (eBook)

Edgar E. Enochs, Overtoun M. G. Jenda (Autoren)

eBook Download: PDF

2011
108 Seiten
De Gruyter (Verlag)
978-3-11-021523-6 (ISBN)

Infos

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.

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

Autor

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

Inhalt

Preface 8
Nomenclature 10
1 Complexes of Modules 14
1.1 Definitions and Basic Constructions 14
1.2 Complexes Formed from Modules 17
1.3 Free Complexes 19
1.4 Projective and Injective Complexes 20
1.5 Exercises 24
2 Short Exact Sequences of Complexes 26
2.1 The Groups Extn(C,D) 26
2.2 The Group Ext1(C,D) 29
2.3 The Snake Lemma for Complexes 35
2.4 Mapping Cones 37
2.5 Exercises 38
3 The Category K (R-Mod) 40
3.1 Homotopies 40
3.2 The Category K(R-Mod) 41
3.3 Split Short Exact Sequences 43
3.4 The Complexes Hom (C,D) 46
3.5 The Koszul Complex 48
3.6 Exercises 49
4 Cotorsion Pairs and Triplets in C(R-Mod) 50
4.1 Cotorsion Pairs 50
4.2 Cotorsion Triplets 55
4.3 The Dold Triplet 57
4.4 More on Cotorsion Pairs and Triplets 58
4.5 Exercises 61
5 Adjoint Functors 62
5.1 Adjoint Functors 62
5.2 Exercises 67
6 Model Structures 68
6.1 Model Structures on C(R-Mod) 68
6.2 Exercises 77
7 Creating Cotorsion Pairs 79
7.1 Creating Cotorsion Pairs in C(R-Mod) in a Termwise Manner 79
7.2 The Hill Lemma 80
7.3 More Cotorsion Pairs 85
7.4 More Hovey Pairs 88
7.5 Exercises 89
8 Minimal Complexes 91
8.1 Minimal Resolutions 91
8.2 Decomposing a Complex 94
8.3 Exercises 95
9 Cartan and Eilenberg Resolutions 96
9.1 Cartan–Eilenberg Projective Complexes 96
9.2 Cartan and Eilenberg Projective Resolutions 98
9.3 C–E Injective Complexes and Resolutions 101
9.4 Cartan and Eilenberg Balance 102
9.5 Exercises 102
Bibliographical Notes 104
Bibliography 106
Index 108

Rezensionen

lt;P>"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

Produkt-Details

• Erscheint lt. Verlag: 29.8.2011
• Reihe/Serie: De Gruyter Expositions in Mathematics
• Reihe/Serie: De Gruyter Expositions in Mathematics
• Reihe/Serie: ISSN
• Reihe/Serie: ISSN
• Verlagsort: Berlin/Boston
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Geschichte
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• Schlagworte: Algebra • category • Complex • functor • Funktor • Kategorie • Modul
• ISBN-10: 3-11-021523-3 / 3110215233
• ISBN-13: 978-3-11-021523-6 / 9783110215236