Let $ R $ be a commutative noetherian ring. Denote by $\operatorname {mod} R $ the
category of finitely generated $ R $-modules, by $\operatorname {D^ b}(R) $ the bounded …

Firstly, we compare the bounded derived categories with respect to the pure-exact and the
usual exact structures, and describe bounded derived category by pure-projective modules …

Relations between Gorenstein derived categories, Gorenstein defect categories and
Gorenstein stable categories are established. Using these, the Gorensteinness of an …

We introduce the singularity category with respect to Ding projective modules, D dpsg b (R),
as the Verdier quotient of Ding derived category D DP b (R) by triangulated subcategory K b …

Abstract Let A, A′, and A ″be artin algebras. We prove that if there is a recollement of the
bounded Gorenstein derived category DG (P (Mod A)) b (Mod A) relative to the bounded …

Invariants with respect to recollements of the stable category of Gorenstein projective A-
modules over an algebra A and stable equivalences are investigated. Specifically, the …

We introduce the relative Gorenstein defect category of an abelian category with respect to
an admissible subcategory, generalizing the Gorenstein defect categories of PA Bergh, D …

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62¹ 2 数学学ª « Vol.62, No.2 2019 3月 ACTA MATHEMATICA SINICA, CHINESE SERIES …

In this paper we study the relation between Gorenstein derived and pure derived categories
under some conditions. Then, we also study the relation between Gorenstein singularity and …

抄録 Let be an abelian category with enough projective objects and an additive and full
subcategory of, and let be the Gorenstein category of. We study the properties of the-derived …