Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using t...Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.展开更多
This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationsh...This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.展开更多
In this paper, we investigate Ding projective dimensions and Ding injective di- mensions of modules and rings. Let R be a ring with rDPD（R） = n 〈 ∞, and let YYl = {Mild（M） 〈 ∞}. We prove that （DP,W1） is a co...In this paper, we investigate Ding projective dimensions and Ding injective di- mensions of modules and rings. Let R be a ring with rDPD（R） = n 〈 ∞, and let YYl = {Mild（M） 〈 ∞}. We prove that （DP,W1） is a complete hereditary cotorsion pair such that a module M belongs to DD∩W1 if and only if M is projective, moreover, 1421 = （M[pd（M） 〈 ∞} = {MIfd（M） ≤ n} = {MIpd（M） ≤ n}. Then we introduce and inves- tigate Ding derived functor Dext^i（-, -）, and use it to characterize global Ding dimension. We show that if R is a Ding-Chen ring, or if R is a ring with rDPD（R） 〈≤ and rDID（R） 〈 ≤, then rDPD（R） 〈 n if and only if rDID（R） 〈 n if and only if Dext^n＋i（M,N） = 0 for all modules M and N and all integer i ≥ 1.展开更多
In the paper, Ding projective modules and Ding projective complexes are considered. In particular, it is proven that Ding projective complexes are precisely the complexes X for which each Xm is a Ding projective R-mod...In the paper, Ding projective modules and Ding projective complexes are considered. In particular, it is proven that Ding projective complexes are precisely the complexes X for which each Xm is a Ding projective R-module for all m ∈ Z.展开更多
Abstract We introduce the singularity category with respect to Ding projective modules, Db dpsg（R）, as the Verdier quotient of Ding derived category Db DP（R） by triangulated subcategory Kb（DP）, and give some tri...Abstract We introduce the singularity category with respect to Ding projective modules, Db dpsg（R）, as the Verdier quotient of Ding derived category Db DP（R） by triangulated subcategory Kb（DP）, and give some triangle equivalences. Assume DP is precovering. We show that Db DP（R） ≌K-,dpb（DP） and Dbpsg（R） ≌ DbDdefect（R）. We prove that each R-module is of finite Ding projective dimension if and only if Dbdpsg（R） = 0.展开更多
Let R→S be a ring homomorphism and X be a complex of R-modules.Then the complex of S-modules S L RX in the derived category D(S)is constructed in the natural way.This paper is devoted to dealing with the relationship...Let R→S be a ring homomorphism and X be a complex of R-modules.Then the complex of S-modules S L RX in the derived category D(S)is constructed in the natural way.This paper is devoted to dealing with the relationships of the Gorenstein projective dimension of an R-complex X(possibly unbounded)with those of the S-complex S■R^L X.It is shown that if R is a Noetherian ring of finite Krull dimension and :R→S is a faithfully flat ring homomorphism,then for any homologically degree-wise finite complex X,there is an equality GpdRX=GpdS(S■R^LX).Similar result is obtained for Ding projective dimension of the S-complex S■R^L X.展开更多
文摘Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.
基金Supported by the Postdoctoral Science Foundation of China（2017M611851）, the Jiangsu Planned Projects for Postdoctoral Research Funds（1601151C） and the Provincial Natural Science Foundation of Anhui Province（KJ2017A040）
文摘This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.
基金Supported by the National Natural Science Foundation of China(11201424)the Zhejiang Natural Science Foundation of China(LY12A01026)
文摘In this paper, we investigate Ding projective dimensions and Ding injective di- mensions of modules and rings. Let R be a ring with rDPD（R） = n 〈 ∞, and let YYl = {Mild（M） 〈 ∞}. We prove that （DP,W1） is a complete hereditary cotorsion pair such that a module M belongs to DD∩W1 if and only if M is projective, moreover, 1421 = （M[pd（M） 〈 ∞} = {MIfd（M） ≤ n} = {MIpd（M） ≤ n}. Then we introduce and inves- tigate Ding derived functor Dext^i（-, -）, and use it to characterize global Ding dimension. We show that if R is a Ding-Chen ring, or if R is a ring with rDPD（R） 〈≤ and rDID（R） 〈 ≤, then rDPD（R） 〈 n if and only if rDID（R） 〈 n if and only if Dext^n＋i（M,N） = 0 for all modules M and N and all integer i ≥ 1.
基金Supported by National Natural Science Foundation of China(Grant Nos.11561039 and 11761045)Natural Science Foundation of Gansu Province of China(Grant No.17JR5RA091)
文摘In the paper, Ding projective modules and Ding projective complexes are considered. In particular, it is proven that Ding projective complexes are precisely the complexes X for which each Xm is a Ding projective R-module for all m ∈ Z.
基金Supported by National Natural Science Foundation of China(Grant Nos.11261050,11361051 and 11361052)Program for New Century Excellent Talents in University(Grant No.NCET-13-0957)
文摘Abstract We introduce the singularity category with respect to Ding projective modules, Db dpsg（R）, as the Verdier quotient of Ding derived category Db DP（R） by triangulated subcategory Kb（DP）, and give some triangle equivalences. Assume DP is precovering. We show that Db DP（R） ≌K-,dpb（DP） and Dbpsg（R） ≌ DbDdefect（R）. We prove that each R-module is of finite Ding projective dimension if and only if Dbdpsg（R） = 0.
基金supported by the National Natural Science Foundation of China(Nos.11261050,11561061).
文摘Let R→S be a ring homomorphism and X be a complex of R-modules.Then the complex of S-modules S L RX in the derived category D(S)is constructed in the natural way.This paper is devoted to dealing with the relationships of the Gorenstein projective dimension of an R-complex X(possibly unbounded)with those of the S-complex S■R^L X.It is shown that if R is a Noetherian ring of finite Krull dimension and :R→S is a faithfully flat ring homomorphism,then for any homologically degree-wise finite complex X,there is an equality GpdRX=GpdS(S■R^LX).Similar result is obtained for Ding projective dimension of the S-complex S■R^L X.
