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Abstract
Let R be a ring, M a right R-module, and n a fixed non-negative integer. M is called n-cotorsion if for any flat right R-module N. M is said to be n-flat if
for any n-cotorsion right R-module N. We prove that (ℱ
n
,
n
) is a complete hereditary cotorsion theory, where ℱ
n
(resp.
n
) denotes the class of all n-flat (resp. n-cotorsion) right R-modules. Several applications are given.
Keywords:
ACKNOWLEDGMENTS
This research was partially supported by Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 200520284015, 20030284033), EYTP and NNSF of China (No. 10331030) and by the Nanjing Institute of Technology of China. The authors would like to thank the referee for the comments and suggestions.
Notes
Communicated by R. Wisbauer.