Matrix Rings with Summand Intersection Property

A ring R has right SIP (SSP) if the intersection (sum) of two direct summands of R is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of R by M has SIP if and only if R has SIP and (1 – e)Me = 0 for every idempotent e in R. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.     

具有性质(G'_k)的Wakamatsu倾斜模

本文引进了具有性质(G'k)的Wakamatsu倾斜模的概念,并用同调有限子范畴的性质对其进行了刻画．     

Finite-Dimensional Simple Leibniz Pairs and Simple Poisson Modules

Simple modules over the Leibniz pairs are studied. Simple Poisson modules over Poisson algebras of the semisimple associative algebra structure are determined and they are nothing but simple bimodules over simple associative algebras with standard noncommutative Poisson algebra structure.     

The core of zero-dimensional monomial ideals

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

Hopf代数上的扭曲模和(斜)余配对Hopf模

本文第一部分主要把扭曲的方法运用到模上,从而得到扭曲模．作为特例,我们构造了H  M的Smaush模和量子模．当K是有限维Hopf代数,证明K*  M是一个右D(K)-Hopf模,因此得到了一个基本同构定理．第二部分主要把斜余配对双代数进行推广,得到了斜余配对Hopf模,并且给出判断斜余配对Hopf模的一个充要条件．     

Structure control within poly(amidoamine) dendrimers: size, shape and regio-chemical mimicry of globular proteins

This work describes the syntheses of a new poly(amidoamine) (PAMAM) dendrimer family possessing a disulfide function (cystamine) in its core. Traditional redox-chemistry associated with the disulfide core in these dendrimer structures, provides a versatile strategy for designing unique sizes, shapes and controlling the regio-disposition of chemical groups on the surface of these dendrimers. Various single site, sulfhydryl functionalized dendron reactants may be generated in situ, under standard reducing conditions (i.e. dithiothreitol (DTT)). Facile control of size, shape and chemical functionality placement involves covalent hybridization of these single point, sulfhydryl reactive dendron components. This is accomplished by re-oxidation in the presence of air, to yield generation/surface chemistry differentiated cross-over products which may be isolated by preparative thin layer or column chromatography. Differentiated cystamine core dendrimers derived from combination and permutation of lower generation (i.e. Gen.=0-3) sulfhydryl functionalized dendrons possessing amino, hydroxyl, acetamido or dansyl surface groups, were synthesized and isolated. They were characterized by a variety of methods including; ¹³C NMR, capillary electrophoresis (CE), gel electrophoresis (PAGE), thin layer chromatography (TLC) and electrospray (ES) or matrix assisted laser desorption ionization (MALDI-TOF) mass spectrometry. This general strategy has broad implications for the systematic size, shape and regio-chemical control of a wide range of dendritic nanostructures, many of which may be designed to mimic the sizes, shapes and regio specific chemo-domains observed for globular proteins.     

Contravariant forms and extremal projectors

Tensor product of irreducible modules of highest weight over a semi-simple quantum group is completely reducible if and only if a natural contravariant form is non-degenerate when restricted to the span of singular vectors. We express this restriction through the extremal projector of the quantum group providing a computationally feasible criterion for complete reducibility of tensor products.     

Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

Construction of Graded Covariant GL(m/n) Modules Using Tableaux

Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on V ^l . The isomorphism between this group of actions and the symmetric group S _l enables the graded generalization of the Young symmetrizers, and hence of the column relations and Garnir relations, to be made. Consequently, corresponding to each partition of l an irreducible GL(m/n) module may be obtained as a submodule of V ^l . A basis for the module labeled by the partition is provided by GL(m/n)–standard tableaux of shape defined by Berele and Regev. The reduction of an arbitrary tableau to standard form is accomplished through the use of graded column relations and graded Garnir relations. The standardization procedure is algorithmic and allows matrix representations of the Lie superalgebras gl(m/n) and sl(m/n) to be constructed explicitly over the field of rational numbers. All the various steps of the standardization algorithm are exemplified, as well as the explicit construction of matrices representing particular elements of gl(m/n) and sl(m/n).