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
For the existing support vector machine, when recognizing more questions, the shortcomings of high computational complexity and low recognition rate under the low SNR are emerged. The characteristic parameter of the s...For the existing support vector machine, when recognizing more questions, the shortcomings of high computational complexity and low recognition rate under the low SNR are emerged. The characteristic parameter of the signal is extracted and optimized by using a clustering algorithm, support vector machine is trained by grading algorithm so as to enhance the rate of convergence, improve the performance of recognition under the low SNR and realize modulation recognition of the signal based on the modulation system of the constellation diagram in this paper. Simulation results show that the average recognition rate based on this algorithm is enhanced over 30% compared with methods that adopting clustering algorithm or support vector machine respectively under the low SNR. The average recognition rate can reach 90% when the SNR is 5 dB, and the method is easy to be achieved so that it has broad application prospect in the modulating recognition.展开更多
Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top s...Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top space V） is determined, where the highest weightof H（n）<sub>0</sub>-module V is not kλ<sub>1</sub> for any nonnegative integer k.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
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
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
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.
Let W(Г)be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+...Let W(Г)be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+δ_(α+β,0)δ_(i+j),0α^(3)-α/12 C and[C,L_(α,i)]=0.In this paper,W(Г)-modules of the intermediate series satisfying some conditions are constructed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.展开更多
Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslan- der and Bridger and the Coh...Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslan- der and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module w and the finitistic dimension with respect to w.展开更多
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supported in part by the National Natural Science Foundation of China under Grand No.61871129 and No.61301179Projects of Science and Technology Plan Guangdong Province under Grand No.2014A010101284
文摘For the existing support vector machine, when recognizing more questions, the shortcomings of high computational complexity and low recognition rate under the low SNR are emerged. The characteristic parameter of the signal is extracted and optimized by using a clustering algorithm, support vector machine is trained by grading algorithm so as to enhance the rate of convergence, improve the performance of recognition under the low SNR and realize modulation recognition of the signal based on the modulation system of the constellation diagram in this paper. Simulation results show that the average recognition rate based on this algorithm is enhanced over 30% compared with methods that adopting clustering algorithm or support vector machine respectively under the low SNR. The average recognition rate can reach 90% when the SNR is 5 dB, and the method is easy to be achieved so that it has broad application prospect in the modulating recognition.
基金Project supported by the National Natural Science Foundation of China.
文摘Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top space V） is determined, where the highest weightof H（n）<sub>0</sub>-module V is not kλ<sub>1</sub> for any nonnegative integer k.
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）.
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.
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.
基金Supported by NSF grants 11431010 and 11971350 of China.
文摘Let W(Г)be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+δ_(α+β,0)δ_(i+j),0α^(3)-α/12 C and[C,L_(α,i)]=0.In this paper,W(Г)-modules of the intermediate series satisfying some conditions are constructed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20100091110034)National Natural Science Foundation of China (Grant No. 11171142)+1 种基金Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK2010047, BK2010007)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslan- der and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module w and the finitistic dimension with respect to w.
