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Relative Left Derived Functors of Tensor Product Functors 被引量:1
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作者 Jun Fu WANG Zhao Yong HUANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第7期753-764,共12页
We introduce and study the relative lett derive functor Torn(£,£1) category, which unifies several related left derived functors. Then we give some criteria for computing the -resolution dimensions of modules in t... We introduce and study the relative lett derive functor Torn(£,£1) category, which unifies several related left derived functors. Then we give some criteria for computing the -resolution dimensions of modules in terms of the properties of Torn(£,£1) . We also construct a complete and hereditary cotorsion pair relative to balanced pairs. Some known results are obtained as corollaries. 展开更多
关键词 Tensor product functors relative left derived functors balanced pairs cotorsion pairs (co)resolution dimension
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On Ding homological dimensions 被引量:1
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作者 ZHU Hai-yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第4期491-502,共12页
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
关键词 Ding projective (injective) dimension cotorsion pair derived functor.
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On the Homology of the Dual de Rham Complex
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作者 Roman MIKHAILOV 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2022年第10期1666-1676,共11页
We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a correc... We study the homology of the dual de Rham complex as functors on the category of abelian groups.We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean’s computations of the zeroth homology group. 展开更多
关键词 Dual de Rham complex polynomial functor divided powers derived functors
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Preservation of Quasi-isomorphisms of Complexes
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作者 Zhong Kui LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第12期2489-2500,共12页
We consider the preservation property of the homomorphism and tensor product functors for quasi-isomorphisms and equivalences of complexes. Let X and Y be two classes of R-modules with Ext〉I(X,Y) = 0 for each objec... We consider the preservation property of the homomorphism and tensor product functors for quasi-isomorphisms and equivalences of complexes. Let X and Y be two classes of R-modules with Ext〉I(X,Y) = 0 for each object X ∈ X and each object Y ∈ Y. We show that if A,B ∈ C^(R) are X-complexes and U, V ∈ Cr(R) are Y-complexes, then U V Hom(A, U) Hom(A, Y); A B Hom(B, U) Hom(A, U). As an application, we give a sufficient condition for the Hom evaluation morphism being invertible. 展开更多
关键词 Quasi-isomorphism equivalence derived functor Gorenstein homological dimension Hom evaluation morphism
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