Divisor Theory in Module Categories - 1st Edition - ISBN: 9780720427158, 9781483257204

Divisor Theory in Module Categories

1st Edition

Authors: W. V. Vasconcelos
Editors: Leopoldo Nachbin
eBook ISBN: 9781483257204
Imprint: North Holland
Published Date: 1st January 1974
Page Count: 130
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Description

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

Bibliography

Index

Details

No. of pages:
130
Language:
English
Copyright:
© North Holland 1974
Published:
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