Cartan-Eilenberg complexes and Auslander categories

الأصل · EN

Let R be a commutative noetherian ring with a semi-dualizing module C. The Auslander categories with respect to C are related through Foxby equivalence: @C=50ptAC(R) @<0.4ex>[r]ᶜ⊗ˡᵣ ⁻ & BC(R) @<0.4ex>[l]RHomᵣ(C, -). We firstly intend to extend the Foxby equivalence to Cartan-Eilenberg complexes. To this end, C-E Auslander categories, C-E W complexes and C-E W-Gorenstein complexes are introduced, where W denotes a self-orthogonal class of R-modules. Moreover, criteria for finiteness of C-E Gorenstein dimensions of complexes in terms of resolution-free characterizations are considered.