Abstract
Let ℒ1 ⊇ ℒ2 be classes of right R-modules, we introduce ℒ1-covering modules and projective modules relative to ℒ2 to characterize the relations between the existences of ℒ1-covers, ℒ2-covers and the classes ℒ1, ℒ2. As corollaries, every module in ℱ n is an ℱ-covering module if and only if every flat cover is an ℱ n -cover for each right module if and only if R is a von Neumann regular ring whenever wD(R) < ∞; every flat right R-module is projective relative to 𝒫 if and only if every flat cover is a projective cover for each right module if and only if R is right perfect.
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ACKNOWLEDGMENTS
This research is supported by the Natural Science Foundation of Fujian Province (2009J01003), the Scientific Research Foundation of Fujian Provincial Department of Science and Technology (2007F5038), and the Foundation of Fujian Normal University (2008100209, 09A004).
Notes
Communicated by T. Albu.