On n-Coherent Rings and (n, d)-Rings

Abstract

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat modules and homological dimensions, and use them to characterize right n-coherent rings and right (weak) (n, d)-rings in various way. Some known results can be obtained as corollaries.

Key Words:

• (n, d)-Injective
• (n, d)-Flat
• (n, d)-Ring
• n-Coherent ring

2000 Mathematics Subject Classification:

• 16D10
• 16E40

Acknowledgments

The author wishes to thank Professors Wenting Tong and Weimin Xue for many valuable communications, and the referee for several helpful suggestions. This research is supported by the National Science Foundation of China (A0324656).

Notes

^#Communicated by R. Wisbauer.