Maximal Cohen-Macaulay Modules Over Cohen-Macaulay Rings

ISBN-13: 9780521356947 / Angielski / Miękka / 1990 / 188 str.

Yuji Yoshino; Y. Yoshino; J. W. S. Cassels

Opis

The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.

Recenzje

"In this excellently written book the author presents all the significant algebraic results on this topic....This book gives a careful, self-contained introduction to the theory of maximal Cohen-Macaulay modules readable by research students with thorough knowledge in commutative and general algebra; but it also may serve as a reference work." JÜrgen Herzog, Mathematical Reviews

Spis treści

1. Preliminaries; 2. AR sequences and irreducible morphisms; 3. Isolated singularities; 4. Auslander categories; 5. AR quivers; 6. The Brauer-Thrall theorem; 7. Matrix factorizations; 8. Simple singularities; 9. One-dimensional Cm rings of finite representation type; 10. McKay graphs; 11. Two-dimensional CM rings of finite representation type; 12. Knörrer's periodicity; 13. Grothendieck groups; 14. CM modules on quadrics; 15. Graded CM modules on graded CM rings; 16. CM modules on toric singularities; 17. Homogeneous CM rings of finite representation type; Addenda; References.