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Torsion Theories over Commutative Rings

by W. Brandal and E. Barbut

This book gives a clear and readable account of the current state of the art for torsion theories dealing with commutative rings and the decompositions of modules.

TABLE OF CONTENTS

1. INTRODUCTION
   
2. Chapter 1 Torsion Abelian Groups
   
3. Chapter 2 Torsion Modules over Domains
   
4. Chapter 3 Pretorsion Modules over Commutative Rings
   
5. Chapter 4 The Preradical of a Pretorsion Theory
   
6. Chapter 5 The Category of Pretorsion Modules
   
7. Chapter 6 Rings of Fractions
   
8. Chapter 7 Modules of Fractions
   
9. Chapter 8 Two Decomposition Results
   
10. Chapter 9 Decomposition Torsion Modules into Localizations
    
11. Chapter 10 The Product of Filters
    
12. Chapter 11 Topological Completions
    
13. Chapter 12 Completions and F-local Rings
    
14. Chapter 13 FGC Rings
    
15. Chapter 14 The Spectrum of FGC Rings
    
16. Chapter 15 Basic Filters
    
17. Chapter 16 A Characterization of F-FGC Rings
    
18. Chapter 17 Another Characterization of F-FGC Rings
    
19. Chapter 18 Lifting Idempotents
    
20. Chapter 19 A Third Characterization of F-FGC Rings
    
21. Bibliography
    
22. Index
    

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