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Commutative Coherent Rings / Edition 1

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Overview

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.

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Editorial Reviews

Booknews
Typed monograph provides advanced graduate students of mathematics with a systematic account of essentially all that is presently known concerning a topic which received its name only in 1964. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9783540511151
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 6/5/1989
  • Series: Lecture Notes in Mathematics Series , #1371
  • Edition description: 1989
  • Edition number: 1
  • Pages: 347
  • Product dimensions: 6.00 (w) x 9.10 (h) x 0.90 (d)

Table of Contents

Preliminaries.- to coherence.- Fundamental concepts.- Ring extensions.- Ring constructions and overrings.- Particular coherent rings.- Polynomial rings.- Coherent algebras.

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