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Abstract
We extend the cotorsion dimension of R-modules to unbounded R-complexes by applying the flat model structure on Ch(R) proposed by J. Gillespie. This is not natural because there has been no sufficiently general result available for the existence of proper “cotorsion” resolutions of unbounded complexes, for which one would be able to define the derived functors. The global cotorsion dimension of ring is discussed in our present framework, and the relations between it and other dimensions are investigated as well. Some rings are characterized and some known results are extended.
ACKNOWLEDGMENTS
The research was supported by National Natural Science Foundation of China (No. 10961021) and the Program of Science and Technique, Gansu Province (No. 1010RJZA025). The authors wish to express their sincere thanks for referee for his/her valuable suggestions which lead to Theorem 4.8.
Notes
Communicated by T. Albu.