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Gorenstein Subcategories and Relative Singularity Categories

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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.

abelian categoryself-orthogonalGorenstein subcategoriessemidualizing bimod-ules

Junfu WANG、Tiwei ZHAO

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Changzhou College of Information Technology,Jiangsu 213164,P.R.China

School of Artificial Intelligence,Jianghan University,Hubei 430056,P.R.China

School of Mathematical Sciences,Qufu Normal University,Shandong 273165,P.R.China

Project of Natural Science Foundation of Changzhou College of Information TechnologyProject of Youth Innovation Team of Universities of Shandong Province

CXZK202204Y2022KJ314

2024

10.3770/j.issn:2095-2651.2024.03.004

数学研究及应用
大连理工大学

数学研究及应用

影响因子：0.094
ISSN：2095-2651
年,卷(期)：2024.44(3)
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