Maximal Cohen-Macaulay Modules over Cohen-Macaulay Rings

Y. Yoshino (Author)

9780521356947, Cambridge University Press

Paperback, published 28 June 1990

188 pages
22.8 x 15.3 x 1.5 cm, 0.27 kg

"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

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.

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.

Subject Areas: Algebra [PBF]