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Modules over Non-Noetherian Domains
László Fuchs, Tulane University, New Orleans, LA, and Luigi Salce, University of Padova, Italy
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Mathematical Surveys and Monographs
2001; 613 pp; hardcover
Volume: 84
ISBN-10: 0-8218-1963-1
ISBN-13: 978-0-8218-1963-0
List Price: US$126
Member Price: US$100.80
Order Code: SURV/84
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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 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 advanced-graduate algebra courses and seminars.

Readership

Advanced graduate students and research mathematicians interested in commutative rings and algebras.

Reviews

"The well-written and detailed volume under review deals with a great many topics within the theory of modules over arbitrary non-Noetherian 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 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
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