Non-Noetherian Commutative Ring Theory

  • Scott T. Chapman
  • Sarah Glaz

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

Table of contents

  1. Front Matter
    Pages i-x
  2. Valentina Barucci
    Pages 57-73
  3. Paul-Jean Cahen, Jean-Luc Chabert
    Pages 75-96
  4. Scott T. Chapman, Jim Coykendall
    Pages 97-115
  5. Scott T. Chapman, Michael Freeze, William W. Smith
    Pages 117-137
  6. David E. Dobbs
    Pages 139-168
  7. Marco Fontana, James A. Huckaba
    Pages 169-197
  8. Stefania Gabelli, Evan Houston
    Pages 199-227
  9. Robert Gilmer
    Pages 229-249
  10. William Heinzer, Moshe Roitman
    Pages 287-312
  11. James A. Huckaba, Ira Papick
    Pages 313-323
  12. Gabriel Picavet, Martine Picavet-L’Hermitte
    Pages 369-386
  13. C. Vinsonhaler
    Pages 387-402
  14. Roger Wiegand, Sylvia Wiegand
    Pages 403-428

About this book

Introduction

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

  • Scott T. Chapman
    • 1
  • Sarah Glaz
    • 2
  1. 1.Department of MathematicsTrinity UniversitySan AntonioUSA
  2. 2.Department of MathematicsThe University of ConnecticutStorrsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3180-4
  • Copyright Information Springer-Verlag US 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4835-9
  • Online ISBN 978-1-4757-3180-4
  • About this book