Divisor Theory in Module Categories

Divisor Theory in Module Categories

1st Edition - January 1, 1974

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  • Author: W. V. Vasconcelos
  • eBook ISBN: 9781483257204

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North-Holland Mathematics Studies, 14: Divisor Theory in Module Categories focuses on the principles, operations, and approaches involved in divisor theory in module categories, including rings, divisors, modules, and complexes. The book first takes a look at local algebra and homology of local rings. Discussions focus on Gorenstein rings, Euler characteristics of modules, Macaulay rings, Koszul complexes, Noetherian and coherent rings, flatness, and Fitting's invariants. The text then explains divisorial ideals, including divisors, modules of dimension one, and higher divisorial ideals. The manuscript ponders on spherical modules and divisors and I-divisors. Topics include construction, Euler characteristics of Inj (A), change of rings and dimensions, spherical modules, resolutions and divisors, and elementary properties. The text is a valuable source of information for mathematicians and researchers interested in divisor theory in module categories.

Table of Contents

  • Preface

    Chapter 1 : Local Algebra

    1.1 . Noetherian and Coherent Rings

    1.2 . Local Rings

    1.3 . Flatness

    1.4 . Fitting's Invariants

    Chapter 2 : Homology of Local Rings

    2.1 . Koszul Complexes

    2.2 . Depth

    2.3 . Macaulay Rings

    2.4 . Projective and Injective Dimensions

    2.5 . Euler Characteristics of Modules

    2.6 . Gorenstein Rings

    2.7 . Rings of Type One

    Chapter 3 : Divisorial Ideals

    3.1 . Composition in Id(A)

    3.2 . Divisors

    3.3 . Modules of Dimension One

    Appendix . Higher Divisorial Ideals

    Chapter 4 : Spherical Modules and Divisors

    4.1 . A Theorem of Gruson

    4.2 . Change of Rings and Dimensions

    4.3 . Spherical Modules

    4.4 . Elementary Properties

    4.5 . Resolutions and Divisors

    Chapter 5 : I-Divisors

    5.1 . Construction

    5.2 . Euler Characteristics of Inj(A)

    5.3 .Divisors on Inj(A)o



Product details

  • No. of pages: 130
  • Language: English
  • Copyright: © North Holland 1974
  • Published: January 1, 1974
  • Imprint: North Holland
  • eBook ISBN: 9781483257204

About the Author

W. V. Vasconcelos

Affiliations and Expertise

Rutgers University

About the Editor

Leopoldo Nachbin

Affiliations and Expertise

University of Rochester

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