Synopses & Reviews
In the past two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the subject. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. The general theory is applied to a number of examples and the connections with combinatorics are highlighted. Throughout each chapter, the authors have supplied many examples and exercises.
Synopsis
Now in paperback, this advanced text on Cohen-Macaulay rings has been updated and expanded.
Synopsis
This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.
Synopsis
'This book meets the need for a thorough, concrete, self-contained introduction to the subject. Throughout each chapter the authors have supplied many examples and exercises, which makes the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for specialists also.\n
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Synopsis
'The only modern, broad account of the subject; essential for graduate students and specialists.'
Synopsis
This text emphasizes the study of explicit, specific rings, making the presentation as concrete as possible. The general theory is applied to a number of examples and the connections with combinatorics are highlighted. Throughout each chapter are many examples and exercises.
Table of Contents
1. Regular sequences and depth; 2. Cohen-Macaulay rings; 3. The canonical module. Gorenstein rings; 4. Hilbert functions and multiplicities; 5. Stanley-Reisner rings; 6. Semigroup rings and invariant theory; 7. Determinantal rings; 8. Big Cohen-Macaulay modules; 9. Homological theorems; 10. Tight closure.