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.     

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．     

集合范畴上超滤函子的余代数

定义了集合范畴上的超滤函子F_u(-),并研究了相关性质.包括函子F_u(-)在有限集上保拉回,一个集合的子集成为F_u-子余代数的充要条件,以及两个余代数之间的态射是F_u-余代数同态的充要条件,子集成为子余代数的充要条件,最后以拓扑空间作为F_u-余代数的具体实例,研究了拓扑空间的连续映射与超滤函子的余代数同态之间的关系.     

范畴RMnl上的一个函子

Let _RM_n^l′ be a category which is equivalent to the category of left R-modules.In this paper,we define afunction F:_RM_n^l→_RM_n^l′ and prove that the functor Fpreserves products,direct limits,injections,surjectios and total esactness.Finally,we show that the functor F is a left-adjoint of the inclusion functor I:_RM_n^l′→_RM_n^l. Hence I:_RM_n^l′ is a renective subcategory of _RM_n^l.     

关于函子()~0的注记(英文)

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     

分次环与模范畴上的伴随函子

设 G是有限群 ,R是强 G-分次环 .本文证明了 R Re-与 Hom Re(R,- )都是从模范畴 R - mod到 Re- mod的“纯量”限制函子 F的伴随函子 ,并且两个函子 R Re-和Hom Re(R,- )是自然同构的 .     

关于局部导子的一个注记

本文推广Ｋａｄｉｓｏｎ关于局部导子的一个定理并给出十分简单的证明。     

定义在范畴 RMnl上的张量函数

In this paper, we define a tensor functor on the category of R-n modules, where R is a commutative ring with 1, and prove the following theorems:     

根范畴中的BGP反射函子

在导出范畴和根范畴中定义了BGP反射函子. 用Ringel的Hall代数方法, 应用所定义的BGP反射函子得到Kac-Moody Lie代数上经典的Weyl群作用.     

L—fuzzy模范畴的张量积与张量函子

本文在Ｌ—ｆｕｚｚｙ模范畴中，建立了相应的张量积，给出了它的结构性、存在性与唯一性定理，并讨论了张量函子与Ｈｏｍ函子的伴随性。所得结果为通常张量积的“良好推广”（ｇｏｏｄｅｘｔｅｎｓｉｏｎ）。     

范畴 RMRl上的一个函子及范畴A Grn0

本文定义了一个由范畴 _RM_R^l到范畴Ａ G_rn⁰ 的函子Ｇ，并证明了函子Ｇ保持分量正合及全正合，关于范畴ＡＧG_rn⁰ 证明了定理：     

关于对偶扩张代数有限维数的注记

没A是一个有限维代数，R为A的对偶扩张代数．本我们讨论R的有限维数findim R of R，证明了，在—般情况下findim R≠2findim A，这就回答了惠昌常教授所提的一个问题．     

A Note on Reflexivity

We prove some new results on Hadwin's general version of reflexivity that reduce the study of E-reflexivity (or E-hyperreflexivity) of a linear subspace to a smaller linear subspace. By applying our abstract results, we present a simple proof of D. Hadwin's theorem, which states that every C^∗-algebra is approximately hyperreflexive. We also prove that the image of any C^∗-algebra under any bounded unital homomorphism into the operators on a Banach space is approximately reflexive. We introduce a new version of reflexivity, called approximate algebraic reflexivity, and study its properties.     

A note on the geometry of M 3 and symplectic structures on S 1 × M 3

We investigate the relationship between the geometry of a closed, oriented 3-manifold M and the symplectic structures on S ¹ × M. In most cases the existence of a symplectic structure on S ¹ × M and Thurstonșs geometrization conjecture imply the existence of a geometric structure on M. This observation together with the existence of geometric structures on most 3-manifolds which fiber over the circle suggests a different approach to the problem of finding a fibration of a 3-manifold over the circle in case its product with the circle admits a symplectic structure. This work was supported in part by a GEBIP grant from the Turkish Academy of Sciences and a CAREER grant from the Scientific and Technological Research Council of Turkey.     

A Note on the Abelianization Functor

It is well known that the abelianization of a group G can be computed as the cokernel of the diagonal morphism (1_G, 1_G): G → G × G in the category of groups. We generalize this to arbitrary regular subtractive categories, among which are the category of groups, the category of topological groups, and the categories of other group-like structures. We also establish that an abelian category is the same as a regular subtractive category in which every monomorphism is a kernel of some morphism.     

L 1→ L q Poincaré Inequalities for 0 < q < 1 Imply Representation Formulas

Given two doubling measures μ and ν in a metric space (S, ρ) of homogeneous type, let B ₀⊂S be a given ball. It has been a well-known result by now (see [1–4]) that the validity of an L ¹→L ¹ Poincaré inequality of the following form: for all metric balls B⊂B ₀⊂S, implies a variant of representation formula of fractional integral type: for ρ-a.e. x∈B ₀, One of the main results of this paper shows that an L ¹ to L ^q Poincaré inequality for some 0 < q < 1, i.e., for all metric balls B⊂B ₀, will suffice to imply the above representation formula. As an immediate corollary, we can show that the weak-type condition, also implies the same formula. Analogous theorems related to high-order Poincaré inequalities and Sobolev spaces in metric spaces are also proved. Received December 27, 2000, Accepted May 28, 2001     

On the Diophantine System a^2 ＋ b^2 = c^3 and a^x ＋ b^y = c^z for b is an Odd Prime

Let a, b and c be fixed coprime positive integers. In this paper we prove that if a^2 ＋ b^2 = c^3 and b is an odd prime, then the equation a^x ＋ b^y = c^z has only the positive integer solution （x, y, z） = （2,2,3）.     

The automorphism group of the Toeplitz algebra onH2(T2)

The automorphism group of the C^* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in .