Abstract
Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-injective if Ext d+1 R (P, M) = 0 for any n-presented R-module P. M is said to be (n, d)-projective if Ext1 R (M, N) = 0 for any (n, d)-injective R-module N. We use these concepts to characterize n-coherent rings and (n, d)-rings. Some known results are extended.
ACKNOWLEDGMENTS
This research was partially supported by SRFDP (No. 20050284015, 20030284033), NSFC (No. 10331030), NSF of Jiangsu Province of China (No. BK 2005207), the Postdoctoral Research Fund of China (2005037713), Jiangsu Planned Projects for Postdoctoral Research Fund (0203003403), and the Nanjing Institute of Technology of China. The authors would like to thank Professor Miguel Ferrero for his suggestions.
Notes
Communicated by M. Ferrero.