Abstract
Let (A)be an abelian category,(J)a self-orthogonal subcategory of(A)and each object in(J)admit finite projective and injective dimensions.If the left Gorenstein subcategory l(G)((J))equals to the right orthogonal class of(J)and the right Gorenstein subcategory r(G)((J))equals to the left orthogonal class of(J),we prove that the Gorenstein subcategory(G)((J))equals to the intersection of the left orthogonal class of(J)and the right orthogonal class of(J),and prove that their stable categories are triangle equivalent to the relative singularity category of(A)with respect to(J).As applications,let R be a left Noetherian ring with finite left self-injective dimension and RCs a semidualizing bimodule,and let the supremum of the flat dimensions of all injective left R-modules be finite.We prove that if RC has finite injective(or flat)dimension and the right orthogonal class of C contains R,then there exists a triangle-equivalence between the intersection of C-Gorenstein projective modules and Bass class with respect to C,and the relative singularity category with respect to C-projective modules.Some classical results are generalized.
基金项目
Project of Natural Science Foundation of Changzhou College of Information Technology(CXZK202204Y)
Project of Youth Innovation Team of Universities of Shandong Province(2022KJ314)
NETL
NSTL
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