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Cambridge Studies in Advanced Mathematics Ser.: Cohen-Macaulay Rings by Winfried Bruns and H. Jürgen Herzog (1998, Trade Paperback)
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In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible.
- Buy It NowCambridge Studies in Advanced Mathematics: Series Number 39: Cohen-Macaulay
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521566746
ISBN-139780521566742
eBay Product ID (ePID)687412
Product Key Features
Number of Pages468 Pages
LanguageEnglish
Publication NameCohen-Macaulay Rings
SubjectAlgebra / General
Publication Year1998
FeaturesRevised
TypeTextbook
Subject AreaMathematics
AuthorWinfried Bruns, H. Jürgen Herzog
SeriesCambridge Studies in Advanced Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Height1 in
Item Weight22.4 Oz
Item Length9.1 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
Dewey Edition21
Reviews' … a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of CohenMacaulay rings … very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.' L'Enseignement Mathmatique, ' ... a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings ... very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.'L'Enseignement Mathématique, ' … a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of CohenMacaulay rings … very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.'L'Enseignement Mathématique, 'This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic ... A lot of useful informations are packed also in the exercises which follow each section and in the notes which follow each chapter.'Zentralblatt für Mathematik, ' ... a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings ... very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.' L'Enseignement Mathématique, ' ... a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of CohenMacaulay rings ... very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.' L'Enseignement MathÈmatique, ‘ … a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen–Macaulay rings … very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.’L’Enseignement Mathématique, 'This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic … A lot of useful informations are packed also in the exercises which follow each section and in the notes which follow each chapter.' Zentralblatt fr Mathematik, 'This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic ... A lot of useful informations are packed also in the exercises which follow each section and in the notes which follow each chapter.' Zentralblatt für Mathematik, 'This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic ... A lot of useful informations are packed also in the exercises which follow each section and in the notes which follow each chapter.' Zentralblatt f r Mathematik, ‘This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic … A lot of useful informations are packed also in the exercises which follow each section and in the notes which follow each chapter.’Zentralblatt für Mathematik
Series Volume NumberSeries Number 39
IllustratedYes
Dewey Decimal512.4
Edition DescriptionRevised edition
Table Of Content1. 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.
SynopsisThis 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., In the last 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 homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. 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., 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.
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