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  • © 2011

Commutative Algebra

Noetherian and Non-Noetherian Perspectives

  • Contains a collection of invited survey articles by some of the leading

  • experts in commutative algebra.

  • The included conributions have been carefully selected for their impact on the field.

  • Prepresent various significant developments in both Noetherian and non-Noetherian commutative algebra.

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii
  2. Zero-divisor graphs in commutative rings

    • David F. Anderson, Michael C. Axtell, Joe A. Stickles Jr.
    Pages 23-45
  3. Class semigroups and t-class semigroups of integral domains

    • Silvana Bazzoni, Salah-Eddine Kabbaj
    Pages 47-76
  4. Beyond totally reflexive modules and back

    • Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm
    Pages 101-143
  5. On v-domains: a survey

    • Marco Fontana, Muhammad Zafrullah
    Pages 145-179
  6. Tensor product of algebras over a field

    • Hassan Haghighi, Massoud Tousi, Siamak Yassemi
    Pages 181-202
  7. Direct-sum behavior of modules over one-dimensional rings

    • Ryan Karr, Roger Wiegand
    Pages 251-275
  8. The defect

    • Franz-Viktor Kuhlmann
    Pages 277-318
  9. Almost perfect domains and their modules

    • Luigi Salce
    Pages 363-386
  10. Rees valuations

    • Irena Swanson
    Pages 421-440
  11. Weak normality and seminormality

    • Marie A. Vitulli
    Pages 441-480
  12. Back Matter

    Pages 481-492

About this book

Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra.

 

This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others.

 

This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

Editors and Affiliations

  • , Dipartimento di Matematica, Università degli Studi Roma Tre, Roma, Italy

    Marco Fontana

  • , Department of Mathematics and Statistics, King Fahd University of Petroleum & Mine, Dhahran, Saudi Arabia

    Salah-Eddine Kabbaj

  • , Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

    Bruce Olberding

  • , Department of Mathematics, Reed College, Portland, USA

    Irena Swanson

Bibliographic Information

  • Book Title: Commutative Algebra

  • Book Subtitle: Noetherian and Non-Noetherian Perspectives

  • Editors: Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson

  • DOI: https://doi.org/10.1007/978-1-4419-6990-3

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC 2011

  • Hardcover ISBN: 978-1-4419-6989-7Published: 06 October 2010

  • Softcover ISBN: 978-1-4899-9004-4Published: 10 October 2014

  • eBook ISBN: 978-1-4419-6990-3Published: 29 September 2010

  • Edition Number: 1

  • Number of Pages: VIII, 492

  • Topics: Commutative Rings and Algebras, Algebraic Geometry

Buy it now

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access