Radical of weakly ordered semigroup algebras

We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0- Hecke algebras.     

一类特殊的无限非正则p-群

利用有限正则p-群和局部幂零群的理论,得到:如果G是可解的非正则p-群,且G的每一个无限真子群是正则的,那么群G是秩为p-1的可除阿贝尔群被循环群的扩张.     

The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the “angles” between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the “norm” of the product of the (nonlinear) metric projections onto related convex sets.In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the “linear regularity property” of Bauschke and Borwein, the “normal property” of Jameson (as well as Bakan, Deutsch, and Li’s generalization of Jameson’s normal property), the “strong conical hull intersection property” of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well.     

More on regular linear spaces

We extend the enumeration of regular linear spaces in 1 to at most 19 points. In addition, one of the 5 missing cases in the previous list is settled. The number of regular linear spaces of type (15|2¹⁵,3³⁰) is 10,177,328. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

关于Locale Wallman紧化的一点注记

本文证明了在正规locale范畴中,Banaschewski-Mulvey形式的紧正则反射与Johnstone形式的Wallman紧化一致,从而推广了Johnstone在文献[4]中的主要结果.     

关于强正则环的刻画

通过单边理想是广义弱理想来刻画强正则环,证明了下列条件是等价的:①R是强正则环;②R是半素的左GP-V′-环,且每一个极大的左理想是广义弱理想;③R是半素的左GP-V′-环,且每一个极大的右理想是广义弱理想.     

Representations of distributive semilattices in ideal lattices of various algebraic structures

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000.     

强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何

本文给出了强正则$(\alpha,\beta)-$族的概念,它是[4]和[5]中$SPG-$族概念的推广.进一步,给出了一种用强正则 $(\alpha,\beta)-$族构造强正则$(\alpha,\beta)-$几何的方法.另外,本文还证明了由强正则$(\alpha,\beta)-$线汇构造的强正则$(\alpha,\beta)-$几何是平移强正则$(\alpha,\beta)-$几何;当$t-r>\beta$时,反之亦成立.     

The structure of some classes of <Emphasis Type="Italic">K</Emphasis>-contact manifolds

We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi projectively flat and φ-projectively flat are obtained. We also prove that for a (2n + 1)-dimensional Sasakian manifold the conditions of being quasi projectively flat, φ-projectively flat and locally isometric to the unit sphere S ²ⁿ⁺¹ (1) are equivalent. Finally, we prove that a compact φ-projectively flat K-contact manifold with regular contact vector field is a principal S ¹-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4.