Relative Projective Modules and Relative Injective Modules

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.

Key Words:

• Cotorsion theory
• n-coherent ring
• (n, d)-injective module
• (n, d)-projective module
• (n, d)-ring

2000 Mathematics Subject Classification:

• 16D40
• 16D50
• 16P70

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.