A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes
Abstract
Let R be a commutative noetherian ring, and let C be a semidualizing R-module. In this paper, we study levels of bounded complexes of finitely generated R-modules with respect to the full subcategory GC(R) consisting of Gorenstein C-projective R-modules. Our main result provides a characterization of the Cohen-Macaulayness of R in terms of the finiteness of levels of perfect complexes with respect to GC(R). This recovers a recent theorem of Christensen, Kekkou, Lyle and Soto Levins on the Gorensteinness of R.
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