A Class of Auslander-Regular Macaulay Rings

Abstract

For a (left and right) noetherian semilocal ring R we analyse a regularity concept (called weak regularity) based on the equation gld R = dim R. Examples are regular Cohen-Macaulay orders over a regular local ring, localized enveloping algebras of finite dimensional Lie algebras, and the regular rings classified in Rump (2001b). We prove that weakly regular rings are Auslander-regular and Macaulay.

Key Words:

• Auslander-regular
• Macaulay
• Regular ring

2000 Mathematics Subject Classification:

• Primary: 16P40
• 16L30
• Secondary: 16S30

Acknowledgments