Inspired by Jorgensen et. al., it is proved that if a Cohen-Macaulay local ring R with dualizing module admits a suitable chain of semidualizing R-modules of length n, then R ∼ = Q/(I 1 + · · · + In) for some Gorenstein ring Q and ideals I 1 , · · · , In of Q; and, for each Λ ⊆ [n], the ring Q/(Σ l∈Λ I l ) has some interesting cohomological properties . This extends the result of Jorgensen et. al., and also of Foxby and Reiten. 2010 Mathematics Subject Classification. 13D05, 13D07.
Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule C, C-perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which admit minimal resolutions of C-projective modules.
For a semidualizing module C over a ring R, we study the following classes modulo exact zero divisors: G C -projectives, C ; the Auslander class C ; the Bass class C ; C -projective; C -projective; and C -injective dimensions.
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