环同构及完全保持乘子不动点的映射

令${\mathcal R}_1$, ${\mathcal R}_2$为两个含单位元$I$的环. 在${\mathcal R}_1$某些温和的假设条件下, 本文基于对完全保持乘子不动点映射的分类研究, 给出${\mathcal R}_1$到${\mathcal R}_2$的环同态和环同构的刻画. 然后给出在Banach代数、套代数、矩阵代数以及标准算子代数等算子代数方面的应用.     

CHARACTERISTICS OF THE TRIGONIOIDACEAN EVOLUTION AND THE REGULARITY OF THEIR GENETIC MATERIAL MUTATIONS

The paper discusses the characteristics of the trigonioidacean evolution, including stagecharacter, pattern of the punctuated equilibria, periodic reappearance phenomenon of similarmorphology and synchronous orientation parallelism.This indicates that the trigonioida-ceans were themselves the material foundation cf their evolution.It is pointed out that thecharacteristics reflect the regularity of their genetic material mutations.     

关于A.Menezes和S.Vanstone一文的注记

1987年,R.Schoof对于有限域Fq上的椭圆曲线的同构类数目得出了一个公式.1990年,A.M enezes和S.V anstone对此当q为偶数时给出了一个初等证明.本文利用Burnside引理对q为偶数时给出一个更简单的证明.     

The classification of two-component Cuntz-Krieger algebras

Cuntz-Krieger algebras with exactly one nontrivial closed ideal are classified up to stable isomorphism by the Cuntz invariant. The proof relies on Rørdam's classification of simple Cuntz-Krieger algebras up to stable isomorphism and the author's classification of two-component reducible topological Markov chains up to flow equivalence.

     

Rigidity of measurable structure for \mathbb Z^d-actions by automorphisms of a torus

We show that for certain classes of actions of , by automorphisms of the torus any measurable conjugacy has to be affine, hence measurable conjugacy implies algebraic conjugacy; similarly any measurable factor is algebraic, and algebraic and affine centralizers provide invariants of measurable conjugacy. Using the algebraic machinery of dual modules and information about class numbers of algebraic number fields we construct various examples of -actions by Bernoulli automorphisms whose measurable orbit structure is rigid, including actions which are weakly isomorphic but not isomorphic. We show that the structure of the centralizer for these actions may or may not serve as a distinguishing measure-theoretic invariant. Received: March 12, 2002     

On completion of fuzzy metric spaces

Completions of fuzzy metric spaces (in the sense of George and Veeramani) are discussed. A complete fuzzy metric space Y is said to be a˜fuzzy metric completion of a˜given fuzzy metric space X if X is isometric to a˜dense subspace of Y. We present an example of a˜fuzzy metric space that does not admit any fuzzy metric completion. However, we prove that every standard fuzzy metric space has an (up to isometry) unique fuzzy metric completion. We also show that for each fuzzy metric space there is an (up to uniform isomorphism) unique complete fuzzy metric space that contains a˜dense subspace uniformly isomorphic to it.     

三维空间子群网的推导

在严格的群论基础上对三维空间的两个几何不等价的极大有限群的子群网进行了详细推导.首先对两个极大有限群的所有对称操作矩阵的几何意义进行了逐一分析,然后根据群和子群的关系找出了它们所包含的全部子群,并对这种基于二次型理论的新代数方法的优越性进行了讨论 关键词： 二次型 同构 等价类     

Hyers–Ulam–Rassias stability of a generalized Apollonius–Jensen type additive mapping and isomorphisms between C *‐algebras

Let X, Y be Banach modules over a C *‐algebra. We prove the Hyers–Ulam–Rassias stability of the following functional equation in Banach modules over a unital C *‐algebra: It is shown that a mapping f: X → Y satisfies the above functional equation and f (0) = 0 if and only if the mapping f: X → Y is Cauchy additive. As an application, we show that every almost linear bijection h: A → B of a unital C *‐algebra A onto a unital C *‐algebra B is a C *‐algebra isomorphism when h (2^d uy) = h (2^d u) h (y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The restricted isomorphism problem for metacyclic restricted Lie algebras

Let be a restricted Lie algebra with the restricted enveloping algebra over a perfect field of positive characteristic . The restricted isomorphism problem asks what invariants of are determined by . This problem is the analogue of the modular isomorphism problem for finite -groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacyclic -groups. In this paper, we provide a positive answer to the restricted isomorphism problem in case is metacyclic and -nilpotent.