Mathematical Surveys and Monographs 2001; 613 pp; hardcover Volume: 84 ISBN10: 0821819631 ISBN13: 9780821819630 List Price: US$126 Member Price: US$100.80 Order Code: SURV/84
 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 torsionfree modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pureinjectivity, 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 Prüfer 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 advancedgraduate algebra courses and seminars. Readership Advanced graduate students and research mathematicians interested in commutative rings and algebras. Reviews "The wellwritten and detailed volume under review deals with a great many topics within the theory of modules over arbitrary nonNoetherian commutative integral domains with identity elements ... Many ... results appear here in book form for the first time ... The reviewer heartily recommends this volume."  Mathematical Reviews Table of Contents  Commutative domains and their modules
 Valuation domains
 Prüfer domains
 More nonNoetherian 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 pureinjectivity
 Torsion modules
 Torsionfree modules of finite rank
 Infinite rank torsionfree modules
 Appendix on set theory
 Bibliography
 Author index
 Subject index
