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Abstract
Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be (m,n)-injective if for any (m,n)-presented right R-module P; M is called (m,n)-flat if
for any (m,n)-presented left R-module Q. In this article, M is defined to be (m,n)-projective (resp. (m,n)-cotorsion) if
(resp.
) for any (m,n)-injective (resp. (m,n)-flat) right R-module N. These concepts are used to characterize von Neumann regular rings and (m,n)-coherent rings. Some known results are extended.
ACKNOWLEDGMENTS
This research was partially supported by Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20050284015, 20030284033), NSF of China (No. 10331030), Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0203003403) and the Nanjing Institute of Technology of China.
The authors would like to thank the referee for the valuable comments and suggestions in shaping the article into its present form.
Notes
Communicated by A. Facchini.