算子代数的Cσ性质,C↑～σ性质与自反性

本文首次引入算子集合的Ｃσ性质和Ｃ↑～σ性质的概念，它们与性质Ｃ和性质Ｄσ（１）有一定的关系：两个主要结果是：（１）具有性质Ｃ↑～σ的对偶代数一定是遗传自反的。（２）如果对偶代数所生成的ｎ－自反代数具有性质Ｃσ，则该对偶代数一定是遗传ｎ－自反的。     

算子代数的C_σ性质、C_σ性质与自反性

本文首次引入算子集合的Ｃ＿σ性质和性质的概念，它们与性质Ｃ和性质Ｄ＿σ（１）有一定的关系．两个主要结果是：（１）具有性质Ｃ＿σ的对偶代数一定是遗传自反的．（２）如果对偶代数所生成的ｎ－自反代数具有性质Ｃ＿σ，则该对偶代数一定是遗传ｎ－自反的．     

自反BCK—代数

本文在BCK-代数中引进稳定子的概念，并定义一类特殊的BCK-代数——自反BCK-代数，证明自反BCK-代数的概念与半单BCK-代数的概念是一致的。同时对于有限BCK-代数还得到它是自反的一个充要条件。     

正定关联BCI—代数

本文是作者［１］和［２］的继续，引入了正定关联ＢＣＩ－代数的概念，并证明了：正定关联ＧＢＣＫ－代数类和Ｐ－半单ＢＣＩ－代数类是正定关联ＢＣＩ－代数类的真子类。     

BCK和BCI—代数的映射

在ＢＣＫ－代数中引进了一个右映射和ＢＣＩ－代数中引进了一个弱左映射，并探讨它们的性质。从而推广了文［１］中大部分结果。主要结果是：如果Ｘ是一个ＢＣＫ－代数，Ｙ是一个正定关联ＢＣＫ－代数，则所有Ｘ到Ｙ的左映射的集合也构成一个正定关联ＢＣＫ－代数。     

关于非交换子空间格代数的超自反性

利用Ａｒｖｅｓｏｎ关于自反代数超自反的特征，给出Ｈｉｌｂｅｒｔ空间上一类非交换格自反代数超自反常数的一个估计，证明了一些非交换子空间格自反代数的超自反性．     

自反Banach空间上算子代数的超自反性

本文引入自发Banach空间上算子代数A的超自反定义，讨论了A超自反的充要条件，超自反常数的估计以及超自反在代数同构下的不变性。     

一类有限BCK－代数的序结构

我们在本文中引进了ＢＣＫ－代数的主子代数的概念并证明了关于子代数格的若干结果．作为应用我们给出了ｎ阶ｎ—２型ＢＣＫ－代数的序结构的特征．     

BCI—代数的KI并代数

本文引入ＢＣＩ－代数的ＫＩ并代数，它是ＢＣＫ－代数的无交并的推广。     

自反代数的双局部导子

证明了自反Banach空间X中自反代数A到B(x)的导子集合是拓扑代数双自反的.     

赋范BCK-代数(英文)

引入了BCK-代数的范数与距离的概念,给出了赋范BCK-代数的一些基本性质,证明了赋范BCK-代数的同构(同态)像和原像仍是赋范BCK-代数,研究了BCK-代数与BCK-代数笛卡儿之间的赋范性质关系.并且引入了赋范BCK-代数的点列极限概念,研究了极限的相关性质.讨论了有界赋范BCK-代数的与模糊BCK-代数的关系.     

多值近似空间的上、下近似诱导的拓扑结构

引入了论域U上的自反模糊关系R的传递化表示Rs的概念,利用Rs给出了R和Rs诱导的模糊拓扑的一组共同的基,从而证明了二者诱导的拓扑是相同的,研究了诱导拓扑的度量化问题及其可数性.     

The Reflexive Dimension of a Lattice Polytope

The reflexive dimension refldim(P) of a lattice polytope P is the minimal integer d so that P is the face of some d-dimensional reflexive polytope. We show that refldim(P) is finite for every P, and give bounds for refldim(kP) in terms of refldim(P) and k. Received July 2, 2004     

矩阵方程组$AX=B,XC=D$的Hermitian自反(反Hermitian自反)最小二乘解及其最佳逼近

In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.     

BCK-代数的模糊代数理想

在有界可换BCK-代数上引入了Fuzzy代数理想的概念,给出了Fuzzy代数理想的某些特征,讨论了Fuzzy理想与Fuzzy代数理想的关系。最后描述了全体Fuzzy集的BCK-代数特征。     

Filtrations of Totally Reflexive Modules

In this paper, we introduce a subcategory of totally reflexive modules that have a saturated filtration by other totally reflexive modules. We will prove these are precisely the totally reflexive modules with an upper triangular presentation matrix and that such a module has a complete resolution in which every differential can be simultaneously represented by upper triangular matrices.     

Fuzzy Order Filters in Adjoint Semigroups of BCK-Algebras

In this paper, we introduce the notion of fuzzy order filters in adjoint semigroups of BCK-algebras. We prove that there is a bijection between the fuzzy ideals of BCK-algebras X and the fuzzy order filters in the adjoint semigroup M(X) of X.AMS Subject Classification (2000) 06F35 03G25 20M10     

Generalized Divisors and Total Reflexivity

The notion of generalized divisors on schemes is introduced by Hartshorne. It is shown that there exists a bijection between the set of all generalized divisors on a scheme X and the set of all reflexive coherent 𝒪 _X -modules which are locally free of rank one at generic points. This bijection, corresponds Cartier divisors to the set of all locally free sheaves of rank one. Our aim in this article is to study the class of generalized divisors that maps to totally reflexive coherent 𝒪 _X -modules, under this correspondence. We investigate this class of divisors, that will be called Gorenstein divisors, both over schemes and also over commutative noetherian rings. We show that this class of divisors has usual properties and fits well in the hierarchy of divisors that already exists in the literature.     

Strong Reflexivity of Abelian Groups

A reflexive topological group G is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group G and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.