On finitely injective modules and locally pure-injective modules over Prüfer domains

Over Matlis valuation domains there exist finitely injective modules which are not direct sums of injective modules, as well as complete locally pure-injective modules which are not the completion of a direct sum of pure-injective modules. Over Prüfer domains which are either almost maximal, or -local Matlis, finitely injective torsion modules and complete torsion-free locally pure-injective modules correspond to each other under the Matlis equivalence. Almost maximal Prüfer domains are characterized by the property that every torsion-free complete module is locally pure-injective. It is derived that semi-Dedekind domains are Dedekind.

     

GENERALIZED POWER SERIES MODULES

In this paper we obtain results pertaining to noetherian nature of generalised power series modules over rings not necessarily possessing an indentity element. These considerably strengthen earlier results of Ribenboim on this topic.     

A note on the Auslander-Reiten conjecture

It is proved that the Auslander-Reiten conjecture is true for local Artin algebras with radical cube zero.     

Rad-Projective and Strongly Rad-Projective Modules

We introduce the dual notion to soc-injectivity, namely rad-projective and strongly rad-projective modules. Several interesting results and applications on the new notion are obtained.     

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.     

Labeling the planar face of crystalline cellulose using quantum dots directed by type-I carbohydrate-binding modules

We report a new method for the direct labeling and visualization of crystalline cellulose using quantum dots (QDs) directed by carbohydrate-binding modules (CBMs). Two type-I (surface binding) CBMs belonging to families 2 and 3a were cloned and expressed with dual histidine tags at the N- and C-termini. Semiconductor (CdSe)ZnS QDs were used to label these CBMs following their binding to Valonia cellulose crystals. Using this approach, we demonstrated that QDs are linearly arrayed on cellulose, which implies that these CBMs specifically bind to a planar face of cellulose. Direct imaging has further shown that different sizes (colors) of QDs can be used to label CBMs bound to cellulose. Furthermore, the binding density of QDs arrayed on cellulose was modified predictably by selecting from various combinations of CBMs and QDs of known dimensions. This approach should be useful for labeling and imaging cellulose-containing materials precisely at the molecular scale, thereby supporting studies of the molecular mechanisms of lignocellulose conversion for biofuels production.     

有限复杂度的Koszul代数

首先给出了Koszul代数的张量积的复杂度,然后研究了Koszul遗传代数上的Koszul单列模,并证明了Koszul遗传代数上的Koszul模M的Koszul合成列在同构意义下是唯一的.     

关于广义分次局部上同调的tame性的一个结果

设R=＋n∈N0Rn（R=R0[R1]）是分次Noether交换环,（R0,m0）是一个局部环,R＋=＋n∈NRn;设N是一个有限生成Z-分次R-模,这里N、N0、Z分别表示全体正整数、全体非负整数和全体格致所构成的集合．令h=sup{i∈Z｜HR＋^i（N）不是Artin模}．Dibaei和Nazari证明了HR＋^h（N）是tame模．我们将该结果推广到了广义分次局部上同调模的情形．     

Irreducible weight modules over the twisted Schrödinger-Virasoro algebra

It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.