Modules over Non-Noetherian Domains

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American Mathematical Soc., 2001 - Mathematics - 613 pages
In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prufer domains, but also discuss Krull and Matlis domains, $h$-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.
 

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Contents

Chapter I Commutative Domains and Their Modules
1
Chapter II Valuation Domains
57
Chapter III Prüfer Domains
91
Chapter IV More NonNoetherian Domains
123
Chapter V Finitely Generated Modules
149
Chapter VI Projectivity and Projective Dimension
195
Chapter VII Divisible Modules
247
Chapter VIII Topology and Filtration
273
Chapter XII Polyserial Modules
403
Chapter XIII RDand PureInjectivity
423
Chapter XIV Torsion Modules
463
Chapter XV TorsionFree Modules of Finite Rank
489
Chapter XVI Infinite Rank TorsionFree Modules
531
Appendix on Set Theory
585
Bibliography
591
Author Index
603

Chapter IX Injective Modules
305
Chapter X Uniserial Modules
337
Chapter XI Heights Invariants and Basic Submodules
381

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