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Commutative Coherent Rings

  • Book
  • © 1989

Overview

Authors:
  1. Sarah Glaz
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1371)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XI
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  2. Preliminaries

    • Sarah Glaz
    Pages 1-30

  3. Introduction to coherence

    • Sarah Glaz
    Pages 31-68

  4. Fundamental concepts

    • Sarah Glaz
    Pages 69-107

  5. Ring extensions

    • Sarah Glaz
    Pages 108-148

  6. Ring constructions and overrings

    • Sarah Glaz
    Pages 149-189

  7. Particular coherent rings

    • Sarah Glaz
    Pages 190-227

  8. Polynomial rings

    • Sarah Glaz
    Pages 228-279

  9. Coherent algebras

    • Sarah Glaz
    Pages 280-327

  10. Back Matter

    Pages 328-347
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Commutative Coherent Rings

  • Authors: Sarah Glaz

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0084570

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-51115-1Published: 26 April 1989

  • eBook ISBN: 978-3-540-46159-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 347

  • Topics: K-Theory

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