Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion ...Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion dimension and other homological dimensions. This dimension has nice properties when the ring in consideration is generalized morphic.展开更多
Vertical hot ring rolling(VHRR) process has the characteristics of nonlinearity,time-variation and being susceptible to disturbance.Furthermore,the ring's growth is quite fast within a short time,and the rolled ri...Vertical hot ring rolling(VHRR) process has the characteristics of nonlinearity,time-variation and being susceptible to disturbance.Furthermore,the ring's growth is quite fast within a short time,and the rolled ring's position is asymmetrical.All of these cause that the ring's dimensions cannot be measured directly.Through analyzing the relationships among the dimensions of ring blanks,the positions of rolls and the ring's inner and outer diameter,the soft measurement model of ring's dimensions is established based on the radial basis function neural network(RBFNN).A mass of data samples are obtained from VHRR finite element(FE) simulations to train and test the soft measurement NN model,and the model's structure parameters are deduced and optimized by genetic algorithm(GA).Finally,the soft measurement system of ring's dimensions is established and validated by the VHRR experiments.The ring's dimensions were measured artificially and calculated by the soft measurement NN model.The results show that the calculation values of GA-RBFNN model are close to the artificial measurement data.In addition,the calculation accuracy of GA-RBFNN model is higher than that of RBFNN model.The research results suggest that the soft measurement NN model has high precision and flexibility.The research can provide practical methods and theoretical guidance for the accurate measurement of VHRR process.展开更多
As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generali...As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.展开更多
This paper proved that graded modules for greded division ring R are graded free modules and R is a IBN ring,and if R is a graded commutative ring,RM is a graded module andRM is a finite semisimple module,then gr.inj....This paper proved that graded modules for greded division ring R are graded free modules and R is a IBN ring,and if R is a graded commutative ring,RM is a graded module andRM is a finite semisimple module,then gr.inj.dimRM=inj.dimRM.展开更多
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
Let R be a ring and let H be a.subgroup of a finite group G.We consider the weak global dimension,cotorsion dimension and weak Gorenstein global dimension of the skew group ring R^σ G and its coefficient ring R.Under...Let R be a ring and let H be a.subgroup of a finite group G.We consider the weak global dimension,cotorsion dimension and weak Gorenstein global dimension of the skew group ring R^σ G and its coefficient ring R.Under the assumption that R^σ G is a,separable extension over R^σ H,it is shown that R^σ G and R^σ H share the same homological dimensions.Several known results are then obtained as corollaries.Moreover,we investigate the relationships between the homological dimensions of Ra G and the homological dimensions of a commutative ring R,using the trivial R^σ G-module.展开更多
A commutative Noetherian ring R is called a regular Noetherian ring with pure dimension n, if for any maximal ideal m of R, gl.dimR_m=n, where R_m is the localization of R at the maximal ideal m. It is well known that...A commutative Noetherian ring R is called a regular Noetherian ring with pure dimension n, if for any maximal ideal m of R, gl.dimR_m=n, where R_m is the localization of R at the maximal ideal m. It is well known that if R is a finitely generated commutative algebra over some field, R is integral and gl. dimR【∞, then R is a regular Noetherian ring with pure dimension. Let D(V) be the ring of differential operators over the non-singular n-dimensional irreducible algebraic variety V. Then gr(D(V)) is a展开更多
Let A be a left and right Noetherian ring and let x be a central regular element of A. A_x denotes the localization of A at the central multiplicatively closed subset {1,x,x^2,…}. Suppose M is an A-module such that x...Let A be a left and right Noetherian ring and let x be a central regular element of A. A_x denotes the localization of A at the central multiplicatively closed subset {1,x,x^2,…}. Suppose M is an A-module such that x is a nonzero divisor in. M. It is shown that there is an equality relation among three iniective dimensions ld_A(M), IdA_x(M_x), and I_dA/xA(M/xM). Then the result is applied to the case of Rees rings of filtered rings and an improved and uniform form of the two results of E. K. Ekstrm is obtained. Moreover, the results in this paper generalize the relevant results of Li Huishi, M. Van den Bergh and F. Van Oystaeyen.展开更多
基金supported by Collegial Natural Science Research Program of Education Department of Jiangsu Province (07KJD110043)
文摘Let R be a ring. We define a dimension, called P-cotorsion dimension, for modules and rings. The aim of this article is to investigate P-cotorsion dimensions of modules and rings and the relations between P-cotorsion dimension and other homological dimensions. This dimension has nice properties when the ring in consideration is generalized morphic.
基金Project(51205299)supported by the National Natural Science Foundation of ChinaProject(2015M582643)supported by the China Postdoctoral Science Foundation+2 种基金Project(2014BAA008)supported by the Science and Technology Support Program of Hubei Province,ChinaProject(2014-IV-144)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(2012AAA07-01)supported by the Major Science and Technology Achievements Transformation&Industrialization Program of Hubei Province,China
文摘Vertical hot ring rolling(VHRR) process has the characteristics of nonlinearity,time-variation and being susceptible to disturbance.Furthermore,the ring's growth is quite fast within a short time,and the rolled ring's position is asymmetrical.All of these cause that the ring's dimensions cannot be measured directly.Through analyzing the relationships among the dimensions of ring blanks,the positions of rolls and the ring's inner and outer diameter,the soft measurement model of ring's dimensions is established based on the radial basis function neural network(RBFNN).A mass of data samples are obtained from VHRR finite element(FE) simulations to train and test the soft measurement NN model,and the model's structure parameters are deduced and optimized by genetic algorithm(GA).Finally,the soft measurement system of ring's dimensions is established and validated by the VHRR experiments.The ring's dimensions were measured artificially and calculated by the soft measurement NN model.The results show that the calculation values of GA-RBFNN model are close to the artificial measurement data.In addition,the calculation accuracy of GA-RBFNN model is higher than that of RBFNN model.The research results suggest that the soft measurement NN model has high precision and flexibility.The research can provide practical methods and theoretical guidance for the accurate measurement of VHRR process.
基金Supported by the National Natural Science Foundation of China（11401476） Supported by the Project for Universities of Gansu Province（2015A-019）
文摘As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.
文摘This paper proved that graded modules for greded division ring R are graded free modules and R is a IBN ring,and if R is a graded commutative ring,RM is a graded module andRM is a finite semisimple module,then gr.inj.dimRM=inj.dimRM.
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 Scientific Research Foundation of Hunan Provincial Education Department(no.18C0997).
文摘Let R be a ring and let H be a.subgroup of a finite group G.We consider the weak global dimension,cotorsion dimension and weak Gorenstein global dimension of the skew group ring R^σ G and its coefficient ring R.Under the assumption that R^σ G is a,separable extension over R^σ H,it is shown that R^σ G and R^σ H share the same homological dimensions.Several known results are then obtained as corollaries.Moreover,we investigate the relationships between the homological dimensions of Ra G and the homological dimensions of a commutative ring R,using the trivial R^σ G-module.
基金the National Natural Science Foundation of China.
文摘A commutative Noetherian ring R is called a regular Noetherian ring with pure dimension n, if for any maximal ideal m of R, gl.dimR_m=n, where R_m is the localization of R at the maximal ideal m. It is well known that if R is a finitely generated commutative algebra over some field, R is integral and gl. dimR【∞, then R is a regular Noetherian ring with pure dimension. Let D(V) be the ring of differential operators over the non-singular n-dimensional irreducible algebraic variety V. Then gr(D(V)) is a
文摘Let A be a left and right Noetherian ring and let x be a central regular element of A. A_x denotes the localization of A at the central multiplicatively closed subset {1,x,x^2,…}. Suppose M is an A-module such that x is a nonzero divisor in. M. It is shown that there is an equality relation among three iniective dimensions ld_A(M), IdA_x(M_x), and I_dA/xA(M/xM). Then the result is applied to the case of Rees rings of filtered rings and an improved and uniform form of the two results of E. K. Ekstrm is obtained. Moreover, the results in this paper generalize the relevant results of Li Huishi, M. Van den Bergh and F. Van Oystaeyen.
