Approximation Presentations of Modules and Homological Conjectures

Abstract

In this article we give a sufficient condition of the existence of 𝕎 ^t -approximation presentations. We also introduce property (W ^k ). As an application of the existence of 𝕎 ^t -approximation presentations we give a connection between the finitistic dimension conjecture, the Auslander–Reiten conjecture, and property (W ^k ).

Keywords:

• Homological conjectures
• Property (W ^k )
• Right quasi k-Gorenstein rings
• 𝕎 ^t -approxima-tion presentations

2000 Mathematics Subject Classification:

• 16E10
• 16E30
• 16G10

ACKNOWLEDGMENTS

The research was partially supported by Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060284002), NSF (Grant No. 10771095), and NSF of Jiangsu Province of China (Grant No. BK2005207). The author thanks the referee for the useful and detailed suggestions on this article.

Notes

Communicated by R. Wisbauer