Essentially normal Hilbert modules and K-homology IV: Quasi-homogenous quotient modules of Hardy module on the polydisks

In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modules of H 2 (Dd) are not essentially normal.     

N_(ψ,φ)-type Quotient Modules over the Bidisk

Let H~2■ be the Hardy space over ~the bidisk ■, and let M_(ψ,φ)=[(ψ(z)-φ(w))~2] be the submodule generated by(ψ(z)-φ(w))~2, where ψ(z) and φ(w) are nonconstant inner functions.The related quotient module is denoted by ■. In this paper, we give a complete characterization for the essential normality of N_(ψ,φ). In particular, if ψ(z) = z, we simply write M_(ψ,φ)and N_(ψ,φ) as M_φ and N_φ respectively. This paper also studies compactness of evaluation operators L(0)|N_φand R(0)|N_φ, essential spectrum of compression operator S_z on N_φ, essential normality of compression operators S_z and S_w on N_φ.     

Grbner bases in difference-differential modules and difference-differential dimension polynomials

In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration. We present and verify algorithms for construct-ing these Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner bases on difference-differential mod-ules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.     

Representations of four-derivation Lie algebras of Block type

Block introduced certain analogues of the Zassenhaus algebras over a field of characteristic 0. The nongraded infinite-dimensional simple Lie algebras of Block type constructed by Xu can be viewed as generalizations of the Block algebras. In this paper, we construct a family of irreducible modules in terms of multiplication and differentiation operators on ＂polynomials＂ for four-devivation nongraded Lie algebras of Block type based on the finite-dimensional irreducible weight modules with multiplicity one of general linear Lie algebras. We also find a new series of submodules from which some irreducible quotient modules are obtained.     

A Characterization of Continuous Module Homomorphisms on Random Semi—Normed Modules and Its Applications

In this paper,a characterization of continuous module homomorphisms on random seminormed modules is first given;then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.     

几乎余挠模

In this paper, we introduce the concept of almost cotorsion modules. A module is called almost cotorsion if it is subisomorphic to its cotorsion envelope. Some characterizations of almost cotorsion modules are given. It is also proved that every module is a direct summand of an almost cotorsion module. As an application, perfect rings are characterized in terms of almost cotorsion modules.     

On generalized k-syzygy modules

In this paper, we first introduce the notion of generalized k-syzygy modules, and then give an equivalent characterization that the class of generalized k-syzygy modules coincides with that ofω-k-torsionfree modules. We further study the extension closure of the category consisting of generalized k-syzygy modules. Some known results are obtained as corollaries.     

主拟-Baer模

In this paper, we give the equivalent characterizations of principally quasi-Baer modules, and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer. Moreover, we prove that left principally quasi-Baer rings have Morita invariant property. Connections between Richart modules and principally quasi-Baer modules are investigated.     

M_φ-type Submodules over the Bidisk

Let H~2(D~2) be the Hardy space over the bidisk D~2,and let M_φ=[(z-φ(w))~2] be the submodule generated by(z-φ(w))~2,where φ(w) is a function in H∞(w).The related quotient module is denoted by N_φ=H~2(D~2)ΘM_φ.In the present paper,we study the Fredholmness of compression operators S_z,S_w on N_φ.When φ(w) is a nonconstant inner function,we prove that the Beurling type theorem holds for the fringe operator F_w on [(z-w)~2]Θ z[(z-w)~2] and the Beurling type theorem holds for the fringe operator Fz on M_φΘwM_φ if φ(0)=0.Lastly,we study some properties of F_w on[(z-w~2)~2]Θz[(z-w~2)~2].     

Higher Level Orderings on Modules

The aim of this paper is to investigate higher level orderings on modules over commutative rings. On the basis of the theory of higher level orderings on fields and commutative rings, some results involving existence of higher level orderings are generalized to the category of modules over commutative rings. Moreover, a strict intersection theorem for higher level orderings on modules is established.     

Differential-operator representations of Weyl group and singular vectors in Verma modules

Given a suitable ordering of the positive root system associated with a semisimple Lie algebra,there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module can be interpreted as a differential operator action on polynomials, and thus on the corresponding truncated formal power series. We prove that the space of truncated formal power series gives a differential-operator representation of the Weyl group W. We also introduce a system of partial differential equations to investigate singular vectors in the Verma module. It is shown that the solution space of the system in the space of truncated formal power series is the span of {w(1) | w ∈ W }. Those w(1) that are polynomials correspond to singular vectors in the Verma module. This elementary approach by partial differential equations also gives a new proof of the well-known BGG-Verma theorem.     

限制李超代数的诱导模

In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.     

Extensions of Modules with ACC on d-annihilators

A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a_n)_n of elements of R the ascending chain AnnM(a_1)■ AnnM(a_1 a_2)■AnnM(a_1 a_2 a_3)■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.     

Ghost length, cone length and complete level of DG modules

In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length. We also study some of its upper bounds. The cone length of a DG module is an invariaut closely related with the invariant level. We discover some important results on it.     

AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.     

THE AVERAGE CASE COMPLEXITY OF THE SHIFT-INVARIANT PROBLEM

The present paper deals with the average case, complexity of the shift-invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the techniques proposed by Heinrich(1990). We also point out an essential error regarding the proof of the upper bound in A. G. Werschulz(1991).     

代数整数环的商环

In this paper,we discuss on the algebraic interger ring of the quadratic field of Q.The form of the quotient ring of the algebraic interger ring with respect to the order ideal is presented.     

Toeplitz Products on Bergman–Sobolev Spaces over the Unit Polydisk

In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman–Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces.     

Injective Cogenerators,Cotilting Modules and Cosilting Modules

It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close connections among injective cogenerators,cotilting modules and cosilting modules from the viewpoint of morphism categories.Some applications are also given.     

Some studies on mathematical models for general elastic multi-structures

The aim of this paper is to study the static problem about a general elastic multi-structure composed of an arbitrary number of elastic bodies, plates and rods. The mathematical model is derived by the variational principle and the principle of virtual work in a vector way. The unique solvability of the resulting problem is proved by the Lax-Milgram lemma after the presentation of a generalized Korn's inequality on general elastic multi-structures. The equilibrium equations are obtained rigorously by only assuming some reasonable regularity of the solution. An important identity is also given which is essential in the finite element analysis for the problem.