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Modules over Non-Noetherian Domains
 
László Fuchs Tulane University, New Orleans, LA
Luigi Salce University of Padova, Padova, Italy
Modules over Non-Noetherian Domains
Hardcover ISBN:  978-0-8218-1963-0
Product Code:  SURV/84
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1311-8
Product Code:  SURV/84.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-1963-0
eBook: ISBN:  978-1-4704-1311-8
Product Code:  SURV/84.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Modules over Non-Noetherian Domains
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Modules over Non-Noetherian Domains
László Fuchs Tulane University, New Orleans, LA
Luigi Salce University of Padova, Padova, Italy
Hardcover ISBN:  978-0-8218-1963-0
Product Code:  SURV/84
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1311-8
Product Code:  SURV/84.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-1963-0
eBook ISBN:  978-1-4704-1311-8
Product Code:  SURV/84.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 842001; 613 pp
    MSC: Primary 13;

    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.

  • Table of Contents
     
     
    • Chapters
    • I. Commutative domains and their modules
    • II. Valuation domains
    • III. Prüfer domains
    • IV. More non-noetherian domains
    • V. Finitely generated modules
    • VI. Projectivity and projective dimension
    • VII. Divisible modules
    • VIII. Topology and filtration
    • IX. Injective modules
    • X. Uniserial modules
    • XI. Heights, invariants and basic submodules
    • XII. Polyserial modules
    • XIII. $RD$- and pure-injectivity
    • XIV. Torsion modules
    • XV. Torsion-free modules of finite rank
    • XVI. Infinite rank torsion-free modules
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 842001; 613 pp
MSC: Primary 13;

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.

  • Chapters
  • I. Commutative domains and their modules
  • II. Valuation domains
  • III. Prüfer domains
  • IV. More non-noetherian domains
  • V. Finitely generated modules
  • VI. Projectivity and projective dimension
  • VII. Divisible modules
  • VIII. Topology and filtration
  • IX. Injective modules
  • X. Uniserial modules
  • XI. Heights, invariants and basic submodules
  • XII. Polyserial modules
  • XIII. $RD$- and pure-injectivity
  • XIV. Torsion modules
  • XV. Torsion-free modules of finite rank
  • XVI. Infinite rank torsion-free modules
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.