Cohen–Macaulayness of Rees Algebras of Modules

Abstract

We provide the sufficient conditions for Rees algebras of modules to be Cohen–Macaulay, which has been proven in the case of Rees algebras of ideals in [11] and [4]. As it turns out the generalization from ideals to modules is not just a routine generalization, but requires a great deal of technical development. We use the technique of generic Bourbaki ideals introduced by Simis, Ulrich, and Vasconcelos [14] to obtain the Cohen–Macaulayness of Rees Algebras of modules.

Key Words:

• Analytic spread
• Bourbaki ideal
• Cohen–Macaulay ring
• Rees algebra
• Reduction number

2010 Mathematics Subject Classification:

• 13A30
• 13B22
• 13C14
• 13C15

ACKNOWLEDGMENTS

Part of this work was done when the author was a graduate student at Purdue University under the direction of Professor Bernd Ulrich. The author is very grateful for so many useful suggestions from Professor Ulrich. The author would also like to thank the anonymous referee for detail reading and helpful suggestions to improve the presentation of this article.