Abstract
For a Noetherian ring R and a cotilting R-module T of injective dimension at least 1, we prove that the derived dimension of R with respect to the category XT is precisely the injective dimension of T by applying Auslander–Buchweitz theory and Ghost Lemma. In particular, when R is a commutative Noetherian Cohen–Macaulay local ring with a canonical module ωR and dimR≥1, the derived dimension of R with respect to the category of maximal Cohen–Macaulay modules is precisely dimR.
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