本原环为除环的若干条件(英)

本文推广文［1－3］的结果，给出了本原环为除环的几个条件．     

On free group algebras in division rings with uncountable center

Let be a division algebra with uncountable center . If contains a noncommutative free -algebra, then also contains the -group algebra of the free group of rank 2.

     

Binary electrocatalysts for organic oxidations

The electro-oxidation of formaldehyde and methanol has been studied on a number of binary platinum electrocatalysts. These comprised mixed electro-deposits of Pt with Sb, As, Bi, Hg, Re, Te or Sn and a range of homogeneous Pt-Rh alloys of different, known, surface composition. These systems were found to exhibit an enhanced activity over that of platinum alone, and this behaviour was correlated with the ease of adsorption of oxygen on the added metal. The activities for organic oxidation were compared with predictions of a model involving reaction between adsorbed oxygen and organic species on the metal surface. The proposed mechanism accounts for the behaviour of both homogeneous and heterogeneous alloy systems.     

Modeling Gain Dynamics in EDFAs: Space-Resolved Versus Lumped Models

We present a detailed comparison of dynamic space- and frequency-resolved and lumped erbium-doped fiber amplifier (EDFA) models. The space- and frequency-resolved models are based on an iterative solution of propagation equations for pump, multiple signals, and spectral components of forward and backward propagating amplified spontaneous powers and rate equations for pump, metastable, and ground energy level population densities of erbium ion. In contrast to space-resolved models, the lumped model solves a single ordinary differential equation for time evolution of the length-averaged metastable level population and is therefore substantially less computer time consuming. Both the space, and frequency-resolved and the lumped models give almost identical results when used for an analysis of surviving channel power excursions in concatenated EDFAs fed by multiwavelength signal and add/drop scenarios. For a statistical analysis of output power and signal-tonoise ratio fluctuations in EDFA cascades fed by burst-mode packet traffic, only lumped models can be used.     

A Characterization of the Riesz Probability Distribution

Bobecka and Wesolowski (Studia Math. 152:147–160, [2002]) have shown that, in the Olkin and Rubin characterization of the Wishart distribution (see Casalis and Letac in Ann. Stat. 24:763–786, [1996]), when we use the division algorithm defined by the quadratic representation and replace the property of invariance by the existence of twice differentiable densities, we still have a characterization of the Wishart distribution. In the present work, we show that when we use the division algorithm defined by the Cholesky decomposition, we get a characterization of the Riesz distribution.     

Actions of Solvable Algebraic Groups on Central Simple Algebras

Let k be an algebraically closed base field of arbitrary characteristic. In this paper, we study actions of a connected solvable linear algebraic group G on a central simple algebra Q. The main result is the following: Q can be split G-equivariantly by a finite-dimensional splitting field, provided that G acts “algebraically,” i.e., provided that Q contains a G-stable order on which the action is rational. As an application, it is shown that rational torus actions on prime PI-algebras are induced by actions on commutative domains. Presented by Paul Smith.     

Stereoselective preparation of methylenecyclobutane-fused angular tetracyclic spiroindolines via photosensitized intramolecular [2+2] cycloaddition with allene

Irradiation of 3-(hexa-4,5-dienyl)indole derivatives in the presence of 3′,4′-dimethoxyacetophenone by a high-pressure mercury lamp through Pyrex glass gave the corresponding [2+2] cycloaddition products stereoselectively in high yields. The major product was a methylenecyclobutane-fused angular tetracyclic spiroindoline derivative produced by the [2+2] cycloaddition through a parallel orientation. The minor product was a hexahydromethanocarbazole derivative through a crossed orientation. Electron-withdrawing substituents, such as acyl or alkoxycarbonyl, on the indole nitrogen were suitable for this reaction.     

Power automorphisms of finite p-groups

Abstract

In this paper, the definitions of quasi-orthogonal idempotent sequences and Iq-dimensions of a ring R are given. The relations between Iq-dimensions and block decomposition numbers of a ring are discussed. As a generalization of monic polynomials, the concept of quasi-monic polynomials over a ring is introduced. It is shown that, for a quasi-monic polynomial over a ring, the division algorithm holds. Suslin Lemma and Horrocks' Theorem are extended to the setting of quasi-monic polynomials. For a commutative ring R, if f(x) is a quasi-monic polynomial in R[x], then GD(R) = GD(R[x]/f(x)) is proved, where GD(R) denotes the global dimension of R.     

Real quadratic flexible division algebras

In this paper we give a new process called vectorial isotopy, in order to classify the eight-dimensional real quadratic flexible division algebras, and we solve the isomorphism problem.     

Electrophilic additions to allenes—II : The reaction of benzeneselenenyl chloride with some 1,3-disubstituted allenes

Benzeneselenenyl chloride reacts with 1,3-dialkyl-substituted allenes in methylene chloride solution to give 1:1-adducts. Attack by selenium is found to occur exclusively at the central allenic carbon. In contrast to the analogous reaction of arenesulphenyl chlorides, the preferential formation of the Z-alkene is observed. A mechanism involving the preequilibrium formation of alkylideneseleniranium ions and/or alkylideneepiselenuranes which, in the product-determining step, collapse to products via an anti attack of chloride at the methine carbon of the ring is proposed to account for the preferential formation of the Z-isomers.