Cohen-Macaulay representations / Graham J. Leuschke, Roger Wiegand.

Format:

Book

Author/Creator:

Leuschke, Graham J., 1973-

Contributor:

Wiegand, Roger, 1943-

Series:

Mathematical surveys and monographs ; v. 181.

Mathematical surveys and monographs ; v. 181

Language:

English

Subjects (All):

Cohen-Macaulay modules.

Representations of rings (Algebra).

Physical Description:

xvii, 367 p : illustrations ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2012]

Summary:

Leuschke (Syracuse U.) and Wiegand (U. of Nebraska-Lincoln) explore the representation theory of commutative local rings, specifically the study of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings. Among the topics are semigroups of modules, invariant theory, isolated singularities and dimension two, ascent and descent, and the Brauer-Thrall conjectures. Chapter-end exercises are provided. Basics and background are appended. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)

Contents:

Chapter 1. The Krull-Remak-Schmidt theorem

Chapter 2. Semigroups of modules

Chapter 3. Dimension zero

Chapter 5. Invariant theory

Chapter 6. Kleinian singularities and finite CM type

Chapter 7. Isolated singularities and dimension two

Chapter 8. The double branched cover

Chapter 9. Hypersurfaces with finite CM type

Chapter. 10. Ascent and descent

Chapter 11. Auslander-Buchweitz theory

Chapter 12. Totally reflexive modules

Chapter 13. Auslander-Reiten theory

Chapter 14. Countable Cohen-Macaulay type

Chapter 15. The Brauer-Thrall conjectures

Chapter 16. Finite CM type in higher dimensions

Chapter 17. Bounded CM type

Appendix A.

Basics and background

Appendix B.

Ramification theory.

Notes:

Includes bibliographical references and index.

ISBN:

9780821875810

0821875817

OCLC:

778074251