EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES

Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠ 0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.     

INJECTIVE PRECOVERS AND MODULES OF GENERALIZED INVERSE POLYNOMIALS

Let (S,≤) be an ordered set. Recall that (S,≤) is artinian if every strictly decreasingsequence of elements of S is ?nite, and that (S,≤) is narrow if every subset of pairwiseorder-incomparable elements of S is ?nite. Let S be a commutative monoid. Unl…     

The Peirce decomposition for Jordan quadruple systems

We study the Peirce decomposition for a Jordan quadruple system with respect to a quadripotent and get the multiplication rules for the Peirce spaces.     

On Jordan quadruple systems with quadripotents

The purpose of this article is to show the link between Jordan quadruple systems with quadripotents and Jordan algebras. We also extend the notions of the orthogonality, primitivity, and minimality of tripotents in a Jordan triple system to that of quadripotents in a Jordan quadruple system. We refine the Peirce decomposition of a Jordan quadruple system with respect to a quadripotent to be with respect to a system of orthogonal quadripotents and get the multiplication rules of the Peirce spaces. We show that the notions of primitive and minimal quadripotents coincide in a Jordan quadruple system.     

Compatibility criterion for quadripotents in Jordan quadruple systems

We extend the notion of compatibility of tripotents in a Jordan triple system to that of quadripotents in a Jordan quadruple system and get a criterion for compatibility of quadripotents in a Jordan quadruple system.     

关于复杂度,亏群与不可分解模的若干说明

在本文中，我们给出了CG^ (B)≤2但不满意当p=2时CG^ (B)=CG^-(B)=2的p-可解群的块B的亏群的结构。同时亦给出关于复杂度与不可分解模的若干说明。     

Equations des algèbres Lie triple qui sont des algèbres train

In this paper, we consider equations of Lie triple algebras that are train algebras. We obtain two different types of equations depending on assuming the existence of an idempotent or a pseudo-idempotent.In general Lie triple algebras are not power-associative. However we show that their train equation with an idempotent is similar to train equations of power-associative algebras that are train algebras and we prove that Lie triple algebras that are train algebras of rank $\le 4$ with an idempotent are Jordan algebras.Moreover, the set of non-trivial idempotents has the same expression in Peirce decomposition as that of $e$-stable power-associative algebras.We also prove that the algebra obtained by $2$-gametization process of a Lie triple algebra is a Lie triple one.     

sl(2)的q-变形的不可分解的Harish-Chandra模的分类

本文对sl（2）的q-变形的不可分解的Harish－Chandra模进行了分类．     

广义分解定理与两个不等式

本文给出了Banach空间广义分解定理的一个初等证明,并利用它来证明两个对称不等式.这是首次在Banach空间获得这样的不等式.     

广义正交分解定理与Tseng度量广义逆

本文将Banach空间中广义正交分解定理从线性子空间拓广至非线性集—太阳集,分别给出了一算子为度量投影算子和一度量投影算子为有界线性算子的充要条件;得到了判别Banach空间中子空间广义正交可补的充要条件;建立了王玉文和季大琴(2000年)新近引入的Banach空间中的线性算子的Tseng度量广义逆存在的特征刻划条件;这些工作本质地把王玉文等人的新近结果从自反空间拓广至非自反空间的情形.     

时滞系统的鲁棒性与边界定理

本文首先注意到滞后型拟多项式与中立型拟多项式零点分布的根本区别，并指出一些通常的事实：如特征根对时滞的连续依赖性，所有特征根位于开左半复平面与稳定性的等价关系等对于中立型系统都不成立，然后建立了中立型拟多项式胞鲁棒稳定性的边界定理．依此将可公度时滞中立型系统族的鲁棒稳定性化为相应拟多项式胞所有边的Ｈｕｒｗｉｔｚ稳定性与其中立型项构成的子胞所有边的Ｓｃｈｕｒ稳定性的判定．最后给出了检验中立型胞鲁棒稳定性的一个有效的图解法．     

一个各向异性插值定理及其在二阶问题混合元中的应用

At first this paper presents an interpolate theorem with anisotropic property, which can be applied to estimate the interpolate error based on different directions. Then a discrete mixed form for the second order elliptic problem is constructed.The gradient vector is approximated by non-full piesewise double quadratic polynomials, the function u by piecewise constants only. The advantage is that this scheme is still convergent without regularity assumption of subdivision to domain Ω.     

一个择一定理及对广义凸规划的应用

本文在实线性空间中得出了广义凸函数的择一定理 ,利用这一定理 ,我们获得广义凸规划的最优性条件     

一类二阶抛物型方程初边值问题解的存在定理

本文研究了一类二阶非线性抛物型方程解的存在唯一性问题.利用非线性分析中的吸引盆理论和同胚理论,获得了相应的二阶非线性抛物型方程初边值问题解的大范围存在唯一性定理.     

拓扑度计算定理及其应用

利用半序方法和不动点指数理论,建立了一个非锥映射全连续算子拓扑度为1的新的计算定理.作为应用,考虑了Hammerstein积分方程的非平凡解存在性问题.     

INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

The aim of this paper is to study the conditions by which a P-prime submodule can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.     

FKKM-型定理的推广及应用

本文得到ＦＫＫＭ－型定理的几个新的推广定理,并将所得结果应用于研究重合点问题．文中的结果统一和包含了一些作者的最新成果．     

Banach空间中算子的秩定理

设E和F是Banach空间,B(E,F)表示映E到F的有界线性算子全体.记T0+∈B(F,E)为To∈B(E,F)的一个广义逆.本文证明,每一个具有||T0+(T-T0)|| J<1的算子T∈B(E,F),B≡(I+T0+(T-T0))-1T0+是T的广义逆当且仅当(I-T0+T0)N(T)=N(T0),其中N(·)表示括弧中算子的零空间.这一结果改进了Nashed和Cheng的一个有用的定理,并进一步证明Nashed和Cheng的一个引理对半-Fredholm算子有效但一般未必成立。