Cotorsion Dimension of Unbounded Complexes.

We extend the cotorsion dimension ofR-modules to unboundedR-complexes by applying the flat model structure onCh(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. [ABSTRACT FROM PUBLISHER]