关于(余)反射的范畴性质及其应用

本文研究了（余）反射的范畴性质及应用，得到的主要结果如下：（１）余反射余代数范畴和反射代数范畴是等价的．（２）反射和余反射都具有可扩张性．使用这些结果可以用来推广和化简了［１—４］等人的部分工作．     

三角Hopf代数表示范畴上的Lie余代数

本文在三角Ｈｏｐｆ代数表示范畴上系统地研究了Ｌｉｅ余代数,在此范畴上 的Ｌｉｅ余代数与Ｈｏｐｆ代数之间建立了重要的联系．主要给出了Ｌｉｅ余代数的余包络 余代数的结构．所得结果自然是关于Ｌｉｅ代数的对偶结果,推广了 Ｓｗｅｅｄｌｅｒ Ｍ． Ｅ．, Ｇｕｒｅｖｉｃｈ Ｄ．Ｉ．, Ｍｉｃｈａｅｌｉｓ Ｗ．和 Ｍａｉｉｄ Ｓ．等人的结果．     

三角Hopf代数表示范畴上的Lie余代数

本文在三角Ｈｏｐｆ代数表示范畴上系统地研究了Ｌｉｅ余代数,在此范畴上 的Ｌｉｅ余代数与Ｈｏｐｆ代数之间建立了重要的联系．主要给出了Ｌｉｅ余代数的余包络 余代数的结构．所得结果自然是关于Ｌｉｅ代数的对偶结果,推广了 Ｓｗｅｅｄｌｅｒ Ｍ． Ｅ．, Ｇｕｒｅｖｉｃｈ Ｄ．Ｉ．, Ｍｉｃｈａｅｌｉｓ Ｗ．和 Ｍａｉｉｄ Ｓ．等人的结果．     

对偶余模函子()°和余反射余模

本文给出对偶余模M°的结构刻划及（）°作为逆变函子的左正合性．同时引入余反射余模描述余反射余代数，由此研究余反射余代数的同调性质，证明当char（F）＝0时，F[x1，...，xn]°上的Serre猜测是成立的，即F[x1，...，xn]°的有限余生成内射余模均为余自由的．     

关于μ~H中的Lie双代数和余Poisson-Hopf代数(英文)

本文研究余三角 Ｈｏｐｆ代数余模范畴中的 Ｌｉｅ双代数和余 Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数．我们主要讨论余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数之间的关系．     

关于函子()0的注记

给出了一个对偶余代数问题的反例,作为反射代数的一个应用,建立从卷积代数Ｈｏｍ（Ｃ,Ａ）到余代数张量的对偶代数（Ｃ(?)Ａ⁰）的同构映射     

Hom-可计算余代数的局部化

本文研究了可计算余模和Hom-可计算余代数的局部化问题.利用局部化方法,得到了可计算余模和Hom-可计算余代数的等价条件,推广了余代数上局部化理论的发展.     

关于MH中的Lie双代数和余Poisson-Hopf代数

本文研究余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余ＰｏｉｓｓｏｎＨｏｐｆ代数,我们主要讨论余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数之间的关系。     

超滤函子余代数范畴

研究了超滤函子余代数范畴set_(F_u)的乘积和余积问题.首先构造了集合乘积上的超滤,讨论集合乘积上超滤的存在形式;接着利用超滤函子的性质给出了范畴set_(F_u)的有限乘积以及任意余积构造;最后证明了范畴set_(F_u)的终对象存在.改进了Gumm关于滤子函子的研究结果,深化了相关文献关于超滤函子余代数的研究.     

关于扭曲Lie结构范畴中的对偶函子

首先介绍扭曲Lie余代数．然后讨论扭曲Lie代数和扭曲Lie余代数范畴．主要给出扭曲Lie结构范畴之间函于的一些性质。     

弱代数性自反与强代数性自反

Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.     

算子子空间的渐近自反性和遗传性

研究了算子子空间的渐近自反性问题，渐近自反子空间的遗传斯近自反性以及某些单个算子的渐近自反性．我们也讨论了投影网类的浙近自反性。     

Reflexivity with maximal ideal axes

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. We in this note study rings with the reflexivity whose axis is given by maximal ideals (simply, an RM ring) which are a generalization of symmetric rings. It is first shown that the reflexivity of a ring and the RM ring property are independent of each other, noting that both of them are generalizations of ideal-symmetric rings. We connect RM rings with reflexive rings in various situations raised naturally in the procedure. As a generalization of RM rings, we also study the structure of the reflexivity with the maximal ideal axis on idempotents (simply, an RMI ring) and then investigate the structure of minimal non-Abelian RMI rings (with or without identity) up to isomorphism.     

James sequences and Dependent Choices

We prove James's sequential characterization of (compact) reflexivity in set‐theory ZF + DC , where DC is the axiom of Dependent Choices. In turn, James's criterion implies that every infinite set is Dedekind‐infinite, whence it is not provable in ZF . Our proof in ZF + DC of James' criterion leads us to various notions of reflexivity which are equivalent in ZFC but are not equivalent in ZF . We also show that the weak compactness of the closed unit ball of a (simply) reflexive space does not imply the Boolean Prime Ideal theorem : this solves a question raised in [6]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local Properties of Ternary Rings of Operators and Their Linking C *-Algebras

We show that some local properties (such as nuclearity, exactness, and local reflexivity) of ternary rings of operators (TROs) are closely related to the local properties of their linking C^*-algebras. We also show some equivalent conditions for nuclear TROs, and show that Haagerup's decomposition property for completely bounded maps and Pisier's δ-norm can be naturally generalized to TROs.     

Principle of local reflexivity respecting subspaces

We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting of a Banach space and its subspace.     

全函数空间和置换空间的一些性质

In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.     

General reflexivity and pattern subspaces

This paper extends the theory of reflexivity triples by extending notions and results in the theory of dual operator algebras to this more general setting. In addition, a complete and simple characterization is given for the reflexivity of two-dimensional pattern spaces of finite matrices.     

General reflexivity and pattern subspaces

This paper extends the theory of reflexivity triples by extending notions and results in the theory of dual operator algebras to this more general setting. In addition, a complete and simple characterization is given for the reflexivity of two-dimensional pattern spaces of finite matrices.