Commutative Coherent Rings

  • Authors
  • Sarah Glaz
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1371)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Sarah Glaz
    Pages 1-30
  3. Sarah Glaz
    Pages 31-68
  4. Sarah Glaz
    Pages 69-107
  5. Sarah Glaz
    Pages 108-148
  6. Sarah Glaz
    Pages 149-189
  7. Sarah Glaz
    Pages 190-227
  8. Sarah Glaz
    Pages 228-279
  9. Sarah Glaz
    Pages 280-327
  10. Back Matter
    Pages 328-347

About this book

Introduction

This book provides the first extensive and systematic treatment of the theory of commutative coherent rings. It blends, and provides a link, between the two sometimes disjoint approaches available in the literature, the ring theoretic approach, and the homological algebra approach. The book covers most results in commutative coherent ring theory known to date, as well as a number of results never published before. Starting with elementary results, the book advances to topics such as: uniform coherence, regular rings, rings of small homological dimensions, polynomial and power series rings, group rings and symmetric algebra over coherent rings. The subject of coherence is brought to the frontiers of research, exposing the open problems in the field. Most topics are treated in their fully generality, deriving the results on coherent rings as conclusions of the general theory. Thus, the book develops many of the tools of modern research in commutative algebra with a variety of examples and counterexamples. Although the book is essentially self-contained, basic knowledge of commutative and homological algebra is recommended. It addresses graduate students and researchers.

Keywords

Homological algebra algebra commutative algebra field ring theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0084570
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-51115-1
  • Online ISBN 978-3-540-46159-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book