In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the ...In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the question:When is an essential extension of a finitely presented module(an almost finitely presented module)also finitely presented(almost finitely presented)?In Section 2,we study the C-excellent extensions and the finitely presented dimensions.We obtain some results on the homological dimensions of matrix rings and group rings.展开更多
Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C ...Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.展开更多
Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k....Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k.Various examples and applications are also given.展开更多
Let ∧_(0,0)=(A_BMAANB_B)be a Morita ring,where the bimodule homomorphisms φ and ψ are zero.We study the finite presentedness,locally coherence,pure projectivity,pure injectivity,and FP-injectivity of modules over A...Let ∧_(0,0)=(A_BMAANB_B)be a Morita ring,where the bimodule homomorphisms φ and ψ are zero.We study the finite presentedness,locally coherence,pure projectivity,pure injectivity,and FP-injectivity of modules over A_(0,0).Some applications are then given.展开更多
We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian ...We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause＇s work [Math. Ann., 2012, 353： 765-781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.展开更多
We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented categ...We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.展开更多
Graham Higman posed the question: How small can the integers p and q be made, while maintaining the property that all but finitly many alternating and symmetric groups are factor groups of △(2, p, q)=(x,y: x^2=y^P=(x...Graham Higman posed the question: How small can the integers p and q be made, while maintaining the property that all but finitly many alternating and symmetric groups are factor groups of △(2, p, q)=(x,y: x^2=y^P=(xy)~q=1)? He proved that for a sufficiently large n, the alternating group is a homomorphic image of the triangle group △(2,p, q) where p=3 and q=7. Later, his result was generalized by proving the result for p=3 and q≥7. Choosing p=4 and q≥17 in this paper we have answered the "Hiqman Question".展开更多
基金Supported by the Natural Science Foundation of China
文摘In Section 1 of this paper,we investigate the finitely presented dimension of an essential extension for a module,and obtain results concerning an essential extension of a torsion-free module. We partially answer the question:When is an essential extension of a finitely presented module(an almost finitely presented module)also finitely presented(almost finitely presented)?In Section 2,we study the C-excellent extensions and the finitely presented dimensions.We obtain some results on the homological dimensions of matrix rings and group rings.
文摘Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.
文摘Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k.Various examples and applications are also given.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11671126,12071120).
文摘Let ∧_(0,0)=(A_BMAANB_B)be a Morita ring,where the bimodule homomorphisms φ and ψ are zero.We study the finite presentedness,locally coherence,pure projectivity,pure injectivity,and FP-injectivity of modules over A_(0,0).Some applications are then given.
基金Acknowledgements The author would like to thank his supervisor Professor Zhaoyong Huang, for the valuable help, suggestions, guidance, and encouragement during his studies and preparation of this paper. He also thanks the referees for their careful reading and for pointing out related references. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11571164）.
文摘We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause＇s work [Math. Ann., 2012, 353： 765-781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras.
基金supported by National Natural Science Foundation of China(Grant No.11131001)supported by BIT Basic Scientific Research Grant(Grant No.3170012211408)
文摘We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.
文摘Graham Higman posed the question: How small can the integers p and q be made, while maintaining the property that all but finitly many alternating and symmetric groups are factor groups of △(2, p, q)=(x,y: x^2=y^P=(xy)~q=1)? He proved that for a sufficiently large n, the alternating group is a homomorphic image of the triangle group △(2,p, q) where p=3 and q=7. Later, his result was generalized by proving the result for p=3 and q≥7. Choosing p=4 and q≥17 in this paper we have answered the "Hiqman Question".
