The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes o...The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes on indecomposability of graded modules.展开更多
The graded modules for the Poisson algebras K are inverstigated and their compositionfactors are determined. Also, a revision on the realizations of the irreducible PTG H(n,m)-modules V(n, m) due to Shen is made.
In the category of general monoid graded rings, we propose a new graded radical, i.e. the graded P radical, obtain the structure theorem of corresponding semisimple graded rings, show that it is a graded special ...In the category of general monoid graded rings, we propose a new graded radical, i.e. the graded P radical, obtain the structure theorem of corresponding semisimple graded rings, show that it is a graded special radical and present the graded module characterization of it. Moreover, we investigate the relations between it and reflect P radical.展开更多
In this paper, we characterize the structure of group graded primitive rings having minimal graded one-sided ideals in terms of graded dual modules. We also show that two structure representations of this class of gra...In this paper, we characterize the structure of group graded primitive rings having minimal graded one-sided ideals in terms of graded dual modules. We also show that two structure representations of this class of graded primitive rings are both in a sense uniquely determined by the graded primitive rings considered.展开更多
This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded pa...This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.展开更多
Let R = ⊙n〉0 Rn be a standard graded ring, a ∩ ⊙n〉0 Rn an ideal of R, and M, N two finitely generated graded R-modules. This paper studies the homogeneous components of graded generalized local cohomology modules...Let R = ⊙n〉0 Rn be a standard graded ring, a ∩ ⊙n〉0 Rn an ideal of R, and M, N two finitely generated graded R-modules. This paper studies the homogeneous components of graded generalized local cohomology modules. We show that for any i 〉 0, the n-th graded component Hiα（M, N）n of the i-th generalized local cohomology module of M and N with respect to a vanishes for all n 〉〉 0. Some sufficient conditions are pro- posed to satisfy the equality sup{end（Hiα （M, N）） [ i _〉 0} = sup{end（HiR＋ （M, N）） ｜ i 〉 0}. Also, some sufficient conditions are proposed for the tameness of Hiα（M, N） such that i = fRα＋（M,N） or i = cdα（M,g）, where fRα＋（M,N） and cdα（M,g） denote the R＋- finiteness dimension and the cohomological dimension of M and N with respect to a, respectively. Finally, we consider the Artinian property of some submodules and quotient modules of Hjα（M, N）, where j is the first or last non-minimax level of Hiα（M, N）.展开更多
We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective,then its underlying module over the base ring is Gorenstein projective; the converse holds if the frobenius extensi...We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective,then its underlying module over the base ring is Gorenstein projective; the converse holds if the frobenius extension is either left-Gorenstein or separable(e.g., the integral group ring extension ZZG).Moreover, for the Frobenius extension RA = R[x]/(x^2), we show that: a graded A-module is Gorenstein projective in GrMod(A), if and only if its ungraded A-module is Gorenstein projective, if and only if its underlying R-module is Gorenstein projective. It immediately follows that an R-complex is Gorenstein projective if and only if all its items are Gorenstein projective R-modules.展开更多
The author first constructs a Lie algebra ∑ ：=∑（q, Wd） from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad-1 with coordinates in quantum torus Cqd, and then gives the necessary and suff...The author first constructs a Lie algebra ∑ ：=∑（q, Wd） from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad-1 with coordinates in quantum torus Cqd, and then gives the necessary and sufficient conditions for the highest weight modules to be quasifinite nonzero central charges are Finally the irreducible Z-graded quasifinite ∑-modules with classified.展开更多
Let K be a field and let S = K[x1,...,xn] be a polynomial ring over K. Let F = ir=1 Sei be a finitely generated graded free S-module with basis {e1,..., er} in degrees f1,..., fr such that f1≤ f2 ~≤……≤ fr. We exa...Let K be a field and let S = K[x1,...,xn] be a polynomial ring over K. Let F = ir=1 Sei be a finitely generated graded free S-module with basis {e1,..., er} in degrees f1,..., fr such that f1≤ f2 ~≤……≤ fr. We examine some classes of squarefree monomial submodules of F. Hence, we focalize our attention on the Betti table of such classes in order to analyze the behavior of their extremal Betti numbers.展开更多
Let A and F be artin algebras and ∧UГa paper, we first introduce the notion of k-Gorenstein faithfully balanced selforthogonal bimodule. In this modules with respect to ∧UГ and then characterize it in terms of the...Let A and F be artin algebras and ∧UГa paper, we first introduce the notion of k-Gorenstein faithfully balanced selforthogonal bimodule. In this modules with respect to ∧UГ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext^i （Ext^i （-, U）, U） preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of ∧UГwith finite left or right injective dimension.展开更多
文摘The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes on indecomposability of graded modules.
文摘The graded modules for the Poisson algebras K are inverstigated and their compositionfactors are determined. Also, a revision on the realizations of the irreducible PTG H(n,m)-modules V(n, m) due to Shen is made.
文摘In the category of general monoid graded rings, we propose a new graded radical, i.e. the graded P radical, obtain the structure theorem of corresponding semisimple graded rings, show that it is a graded special radical and present the graded module characterization of it. Moreover, we investigate the relations between it and reflect P radical.
基金Foundation item:The NSF(993521738)of Liaoning Education Department
文摘In this paper, we characterize the structure of group graded primitive rings having minimal graded one-sided ideals in terms of graded dual modules. We also show that two structure representations of this class of graded primitive rings are both in a sense uniquely determined by the graded primitive rings considered.
基金the National Natural Science Foundation of China （Nos. 10371101 10671161）+2 种基金 the Natural Science Foundation of Fujian Province （Nos. Z0511022） and the Foundation of the Education Committee of Fujian Province （Nos. JA050206 JA06008 JB04215）.
文摘This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.
文摘Let R = ⊙n〉0 Rn be a standard graded ring, a ∩ ⊙n〉0 Rn an ideal of R, and M, N two finitely generated graded R-modules. This paper studies the homogeneous components of graded generalized local cohomology modules. We show that for any i 〉 0, the n-th graded component Hiα（M, N）n of the i-th generalized local cohomology module of M and N with respect to a vanishes for all n 〉〉 0. Some sufficient conditions are pro- posed to satisfy the equality sup{end（Hiα （M, N）） [ i _〉 0} = sup{end（HiR＋ （M, N）） ｜ i 〉 0}. Also, some sufficient conditions are proposed for the tameness of Hiα（M, N） such that i = fRα＋（M,N） or i = cdα（M,g）, where fRα＋（M,N） and cdα（M,g） denote the R＋- finiteness dimension and the cohomological dimension of M and N with respect to a, respectively. Finally, we consider the Artinian property of some submodules and quotient modules of Hjα（M, N）, where j is the first or last non-minimax level of Hiα（M, N）.
基金supported by National Natural Science Foundation of China(Grant No.11401476)China Postdoctoral Science Foundation(Grant No.2016M591592)
文摘We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective,then its underlying module over the base ring is Gorenstein projective; the converse holds if the frobenius extension is either left-Gorenstein or separable(e.g., the integral group ring extension ZZG).Moreover, for the Frobenius extension RA = R[x]/(x^2), we show that: a graded A-module is Gorenstein projective in GrMod(A), if and only if its ungraded A-module is Gorenstein projective, if and only if its underlying R-module is Gorenstein projective. It immediately follows that an R-complex is Gorenstein projective if and only if all its items are Gorenstein projective R-modules.
基金Project supported by the Post Doctorate Research Grant from the Ministry of Science and Technologyof China (No. 20060390526)the National Natural Science Foundation of China (No. 10601057)
文摘The author first constructs a Lie algebra ∑ ：=∑（q, Wd） from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad-1 with coordinates in quantum torus Cqd, and then gives the necessary and sufficient conditions for the highest weight modules to be quasifinite nonzero central charges are Finally the irreducible Z-graded quasifinite ∑-modules with classified.
文摘Let K be a field and let S = K[x1,...,xn] be a polynomial ring over K. Let F = ir=1 Sei be a finitely generated graded free S-module with basis {e1,..., er} in degrees f1,..., fr such that f1≤ f2 ~≤……≤ fr. We examine some classes of squarefree monomial submodules of F. Hence, we focalize our attention on the Betti table of such classes in order to analyze the behavior of their extremal Betti numbers.
基金Research partially supported by Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20030284033,20060284002)NSF of Jiangsu Province of China(Grant No.BK2005207)
文摘Let A and F be artin algebras and ∧UГa paper, we first introduce the notion of k-Gorenstein faithfully balanced selforthogonal bimodule. In this modules with respect to ∧UГ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext^i （Ext^i （-, U）, U） preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of ∧UГwith finite left or right injective dimension.
