Modules Over Non-noetherian Domains
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.
- Hardback | 613 pages
- 184.15 x 260.35 x 38.1mm | 1,519.53g
- 15 Nov 2000
- American Mathematical Society
- Providence, United States
Table of contents
Commutative domains and their modules Valuation domains Prufer domains More non-Noetherian domains Finitely generated modules Projectivity and projective dimension Divisible modules Topology and filtration Injective modules Uniserial modules Heights, invariants and basic submodules Polyserial modules RD- and pure-injectivity Torsion modules Torsion-free modules of finite rank Infinite rank torsion-free modules Appendix on set theory Bibliography Author index Subject index.
" ... this volume will be a valuable source of information to workers in [the] field." Bulletin of the London Mathematical Society