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Abstract
Let R be a ring, n a fixed non-negative integer and ℱ the class of all left R-modules of FP-injective dimensions at most n. It is proved that all left R-modules over a left coherent ring R have ℱ-preenvelopes and ℱ-covers. Left (right) ℱ-resolutions and the left derived functors of Hom are used to study the FP-injective dimensions of modules and rings.
ACKNOWLEDGMENTS
The authors are indebted to the referee for various valuable comments leading to improvements of the article. Especially, the referee suggested Theorem 2.11 and a new proof of (4) ⇒ (5) in Theorem 4.10. This research was supported by the National Natural Science Foundation of China (10571026), and the Specialized Research Fund for the Doctoral Program of Higher Education (20060286006).
Notes
Communicated by I. Swanson.