Cohen-Macaulay Rings

ISBN-13: 9780521566742 / Angielski / Miękka / 1998 / 468 str.

Winfried Bruns;Bruns;Jurgen

Opis

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.

Recenzje

'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

Spis treści

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.