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| 1 | Remarks on Gorenstein Weak Injective and Weak Flat Modules显示文摘In this paper,we introduce Gorenstein weak injective and weak flat modules in terms of,respectively,weak injective and weak flat modules;the classes of Gorenstein weak injective and weak flat modules are larger than the classical classes of Gorenstein injective and flat modules.In this new setting,we characterize rings over which all modules are Gorenstein weak injective.Moreover,we discuss the relation between the weak cosyzygy and Gorenstein weak cosyzygy of a module,and also the stability of Gorenstein weak injective modules. | Tiwei Zhao Yunge Xu | 2020 | Algebra Colloquium2020，27，4： | 5 |
| 2 | Special precovered categories of Gorenstein categories显示文摘Let A be an abelian category and P(A)be the subcategory of A consisting of projective objects.Let C be a full,additive and self-orthogonal subcategory of A with P(A)a generator,and let G(C)be the Gorenstein subcategory of A.Then the right 1-orthogonal category G(C)^⊥1 of G(C)is both projectively resolving and injectively coresolving in A.We also get that the subcategory SPC(G(C))of A consisting of objects admitting special G(C)-precovers is closed under extensions and C-stable direct summands(*).Furthermore,if C is a generator for G(C)^⊥1,then we have that SPC(G(C))is the minimal subcategory of A containing G(C)^⊥1∪G(C)with respect to the property(*),and that SPC(G(C))is C-resolving in A with a C-proper generator C. | Tiwei Zhao Zhaoyong Huang | 2019 | Science China Mathematics2019，62，8： | 1 |
| 3 | Homological Dimensions Relative to Special Subcategories显示文摘Let A be an abelian category,C an additive,full and self-orthogonal subcategory of A closed under direct summands,rG(C)the right Gorenstein subcategory of A relative to C,and⊥C the left orthogonal class of C.For an object A in A,we prove that if A is in the right 1-orthogonal class of rG(C),then the C-projective and rG(C)-projective dimensions of A are identical;if the rG(C)-projective dimension of A is finite,then the rG(C)-projective and⊥C-projective dimensions of A are identical.We also prove that the supremum of the C-projective dimensions of objects with finite C-projective dimension and that of the rG(C)-projective dimensions of objects with finite rG(C)-projective dimension coincide.Then we apply these results to the category of modules. | Weiling Song Tiwei Zhao Zhaoyong Huang | 2021 | Algebra Colloquium2021，28，1： | 0 |
| 4 | Complete Cohomology for Extriangulated Categories显示文摘Let(C,E,s)be an extriangulated category with a proper classξof E-triangles.We study complete cohomology of objects in(C,E,s)by applyingξ-projective resolutions andξ-injective coresolutions constructed in(C,E,s).Vanishing of complete cohomology detects objects with finiteξ-projective dimension and finiteξ-injective dimension.As a consequence,we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein.Moreover,we give a general technique for computing complete cohomology of objects with finiteξ-Gprojective dimension.As an application,the relations betweenξ-projective dimension andξ-Gprojective dimension for objects in(C,E,s)are given. | Jiangsheng Hu Dongdong Zhang Tiwei Zhao Panyue Zhou | 2021 | Algebra Colloquium2021，28，4： | 0 |
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