Commutative Coherent Rings (Lecture Notes in Mathematics (1371))

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. Sarah Glaz. Includes Bibliographical References And Index. Annotation 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 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