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Non-Noetherian Commutative Ring Theory

  • Book
  • © 2000

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Editors:
  1. Scott T. Chapman

    1. Department of Mathematics, Trinity University, San Antonio, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Sarah Glaz

    1. Department of Mathematics, The University of Connecticut, Storrs, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. GCD Domains, Gauss’ Lemma, and Contents of Polynomials

    • D. D. Anderson
    Pages 1-31

  3. The Class Group and Local Class Group of an Integral Domain

    • David F. Anderson
    Pages 33-55

  4. Mori Domains

    • Valentina Barucci
    Pages 57-73

  5. What’s New About Integer-Valued Polynomials on a Subset?

    • Paul-Jean Cahen, Jean-Luc Chabert
    Pages 75-96

  6. Half-Factorial Domains, a Survey

    • Scott T. Chapman, Jim Coykendall
    Pages 97-115

  7. On Generalized Lengths of Factorizations in Dedekind and Krull Domains

    • Scott T. Chapman, Michael Freeze, William W. Smith
    Pages 117-137

  8. Recent Progress on Going-Down I

    • David E. Dobbs
    Pages 139-168

  9. Localizing Systems and Semistar Operations

    • Marco Fontana, James A. Huckaba
    Pages 169-197

  10. Ideal Theory in Pullbacks

    • Stefania Gabelli, Evan Houston
    Pages 199-227

  11. Commutative Rings of Dimension 0

    • Robert Gilmer
    Pages 229-249

  12. Finite Conductor Rings with Zero Divisors

    • Sarah Glaz
    Pages 251-269

  13. Construction of Ideal Systems with Nice Noetherian Properties

    • Franz Halter-Koch
    Pages 271-285

  14. Generalized Local Rings and Finite Generation of Powers of Ideals

    • William Heinzer, Moshe Roitman
    Pages 287-312

  15. Connecting Trace Properties

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

  16. Constructing Examples of Integral Domains by Intersecting Valuation Domains

    • K. Alan Loper
    Pages 325-340

  17. Examples Built with D+M, A+XB[X] and other Pullback Constructions

    • Thomas G. Lucas
    Pages 341-368

  18. T-Closedness

    • Gabriel Picavet, Martine Picavet-L’Hermitte
    Pages 369-386

  19. E-Rings and Related Structures

    • C. Vinsonhaler
    Pages 387-402

  20. Prime Ideals and Decompositions of Modules

    • Roger Wiegand, Sylvia Wiegand
    Pages 403-428
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Keywords

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.

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

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