Commutative Coherent Rings

Sarah Glaz (auth.)3540511156, 9783540511151, 0387511156

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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Table of contents :
Preliminaries….Pages 1-30
Introduction to coherence….Pages 31-68
Fundamental concepts….Pages 69-107
Ring extensions….Pages 108-148
Ring constructions and overrings….Pages 149-189
Particular coherent rings….Pages 190-227
Polynomial rings….Pages 228-279
Coherent algebras….Pages 280-327