Envelopes and Covers by Modules of Finite FP-Injective and Flat Dimensions

Lixin Mao Department of Basic Courses, Nanjing Institute of Technology, Nanjing, China; Department of Mathematics, Nanjing University, Nanjing, China

Nanqing Ding Department of Mathematics, Nanjing University, Nanjing, ChinaCorrespondence[email protected]

Abstract

Let R be a ring, n a fixed non-negative integer and ℱ ℐ _n (ℱ _n) the class of all right (left) R-modules of FP-injective (flat) dimension at most n. We prove that ( is a perfect cotorsion theory if R is a right coherent ring with FP-id(R _R) ≤ n. This result was proven by Aldrich, Enochs, Jenda, and Oyonarte in Noetherian case. The modules in are also studied. Some applications are given.

Keywords:

2000 Mathematics Subject Classification:

ACKNOWLEDGMENTS

This research was partially supported by SRFDP (No. 20050284015), NSFC (No. 10331030), China Postdoctoral Science Foundation (No. 20060390926), Collegial Natural Science Research Program of Education Department of Jiangsu Province (No. 06KJB110033), and Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0601021B). The authors would like to thank the referee for the helpful comments and for calling attention to references Aldrich et al. (Citation2001a), Enochs et al. (Citation1998), García Rozas (Citation1999), Hovey (Citation2002), and Pinzon (Citation2005).

Notes

Communicated by R. Wisbauer.

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