Skip to main content
  • Book
  • © 2000

Non-Noetherian Commutative Ring Theory

Part of the book series: Mathematics and Its Applications (MAIA, volume 520)

Buying options

eBook USD 189.00
Price excludes VAT (USA)
  • ISBN: 978-1-4757-3180-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 249.99
Price excludes VAT (USA)
Hardcover Book USD 249.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (21 chapters)

  1. Front Matter

    Pages i-x
  2. Mori Domains

    • Valentina Barucci
    Pages 57-73
  3. What’s New About Integer-Valued Polynomials on a Subset?

    • Paul-Jean Cahen, Jean-Luc Chabert
    Pages 75-96
  4. Half-Factorial Domains, a Survey

    • Scott T. Chapman, Jim Coykendall
    Pages 97-115
  5. On Generalized Lengths of Factorizations in Dedekind and Krull Domains

    • Scott T. Chapman, Michael Freeze, William W. Smith
    Pages 117-137
  6. Recent Progress on Going-Down I

    • David E. Dobbs
    Pages 139-168
  7. Localizing Systems and Semistar Operations

    • Marco Fontana, James A. Huckaba
    Pages 169-197
  8. Ideal Theory in Pullbacks

    • Stefania Gabelli, Evan Houston
    Pages 199-227
  9. Commutative Rings of Dimension 0

    • Robert Gilmer
    Pages 229-249
  10. Generalized Local Rings and Finite Generation of Powers of Ideals

    • William Heinzer, Moshe Roitman
    Pages 287-312
  11. Connecting Trace Properties

    • James A. Huckaba, Ira Papick
    Pages 313-323
  12. T-Closedness

    • Gabriel Picavet, Martine Picavet-L’Hermitte
    Pages 369-386
  13. E-Rings and Related Structures

    • C. Vinsonhaler
    Pages 387-402
  14. Prime Ideals and Decompositions of Modules

    • Roger Wiegand, Sylvia Wiegand
    Pages 403-428

About this book

Commutative Ring Theory emerged as a distinct field of research in math­ ematics only at the beginning of the twentieth century. It is rooted in nine­ teenth century major works in Number Theory and Algebraic Geometry for which it provided a useful tool for proving results. From this humble origin, it flourished into a field of study in its own right of an astonishing richness and interest. Nowadays, one has to specialize in an area of this vast field in order to be able to master its wealth of results and come up with worthwhile contributions. One of the major areas of the field of Commutative Ring Theory is the study of non-Noetherian rings. The last ten years have seen a lively flurry of activity in this area, including: a large number of conferences and special sections at national and international meetings dedicated to presenting its results, an abundance of articles in scientific journals, and a substantial number of books capturing some of its topics. This rapid growth, and the occasion of the new Millennium, prompted us to embark on a project aimed at presenting an overview of the recent research in the area. With this in mind, we invited many of the most prominent researchers in Non-Noetherian Commutative Ring Theory to write expository articles representing the most recent topics of research in this area.

Keywords

  • Dimension
  • Divisor
  • Grad
  • commutative ring
  • ring theory

Editors and Affiliations

  • Department of Mathematics, Trinity University, San Antonio, USA

    Scott T. Chapman

  • Department of Mathematics, The University of Connecticut, Storrs, USA

    Sarah Glaz

Bibliographic Information

Buying options

eBook USD 189.00
Price excludes VAT (USA)
  • ISBN: 978-1-4757-3180-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 249.99
Price excludes VAT (USA)
Hardcover Book USD 249.99
Price excludes VAT (USA)