Residually *-Abelian Valuation with Residue Characteristic Not 2

We are given a division ring D with involution (*) and with a *-valuation V such that V(sx ? xs) > V(sx), for all nonzero elements x, s of D with s = s*. Let χ denote the characteristic of the residue class division ring associated with V. We reported in Theorem 3.2.5 Part 4 in [3 Chacron , M. ( 1989 ). c-Valuations and normal c-orderings . Can. J. Math. XLI : 14 – 67 .[Crossref], [Web of Science ®] , [Google Scholar]] that, in the case χ = 0, either D is a standard quaternion division algebra or else D contains no algebraic elements other than the scalars. In this article, we carry out a generalization of the preceding theorem to the case χ ≠ 2. Our results are fairly complete in the finite dimensional case, and generalize theorems of, notably, J. Graeter and A. I. Lichtman, in the infinite dimensional case.     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

A boolean transfer principle from L*-Algebras to AL*-Algebras

Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is presupposed. MSC: 03C90, 03E40, 17B65, 46L10.     

Cell decomposition for P‐minimal fields

In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p‐adically closed fields. We work here with the notion of P‐minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P‐minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8] (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Note on a Variation of the Schröder-Bernstein Problem for Fields

In this note we study fields F with the property that the simple transcendental extension F(u) of F is isomorphic to some subfield of F but not isomorphic to F. Such a field provides one type of solution of the Schröder-Bernstein problem for fields.     

C~*-代数的迹迹秩

引入C~*-代数迹迹秩的概念,讨论它的基本性质.另外,迹迹秩为零和迹拓扑秩为零的C~*-代数等价,同时讨论这类代数的拟对角扩张性质.设O→I→A→A/I→O是拟对角扩张的短正合列,证明如果TTR(I)≤k且TTR(A/I)=0,则TTR(A)≤k.     

具有卷积的中心自反环

本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张.     

超*BCI-代数的商超代数

修改了超BCI-代数的定义,提出超*BCI-代数并对其性质作了研究.在此基础上,引入超*BCI-代数的左、右扩张、正定对换超*BCI-代数及其陪集等概念,给出了正定对换超*BCI-代数的商超代数定义,y并对其商超代数的性质作了研究.     

Valuation rings and simple transcendental field extensions

If a valuation ring V on a simple transcendental field extension K₀(X) is such that the residue field k of V is not algebraic over the residue field k₀ of V₀=V∩K₀, then for k₀ a perfect field it is shown that k is obtained from k₀ by a finite algebraic followed by a simple transcendental field extension.     

广义四元数体上矩阵的最小多项式

本文给出了广义四元数体上方阵的最小多项式与最小中心多项式的构造公式，讨论了它们的性质及其应用，得到广义四元数方阵相似于对角矩阵的一个充要条件。     

A New Path-Following Algorithm for Nonlinear P*Complementarity Problems

Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119—146], we present in this paper a new path-following method for nonlinear P* complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm tracks the “regularized central path” which exists for any continuous P* problem. It turns out that the algorithm is globally convergent for any P* problem provided that its solution set is nonempty. By different choices of the parameters in the algorithm, the iterative sequence can approach to different types of points of the solution set. Moreover, local superlinear convergence of this algorithm can also be achieved under certain conditions. The research of the first author was supported by The National Natural Science Foundation of China under Grant No. 10201032 and Grant No. 70221001. The research of the second author was supported by Grant CUHK4214/01E, Research Grants Council, Hong Kong. An erratum to this article is available at .     

Deformations of the central extension of the Poisson superalgebra

The Poisson superalgebra realized on smooth Grassmann-valued functions with compact support has a central extension at some values of the superdimension. We find formal deformations of these central extensions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 250–269, August, 2008.     

Algebraic extension of *-A operator

In this paper, we study various properties of algebraic extension of *-A operator. Specifically, we show that every algebraic extension of *-A operator has SVEP and is isoloid. And if T is an algebraic extension of *-A operator, then Weyl's theorem holds for f(T), where f is an analytic functions on some neighborhood of σ(T) and not constant on each of the components of its domain.     

Remarks on Nonassociative Structures in Quantum Projective Field Theory: the Central Extension jl(2,C) of the Double sl(2,C)+sl(2,C) of the Simple Lie Algebra sl(2,C) and Related Topics

This paper is a revised and expanded version of two notes devoted to nonassociative structures in quantum projective field theory.     

基于L~*-格值逻辑上的BCK-代数中直觉不分明化理想

在L~*-格值逻辑的语义框架下,以L~*-格值上的Lukasiewicz蕴涵算子为工具定义了L~*-格值逻辑上的直觉不分明化BCK-代数的概念,将用集论所刻画的BCK-代数中理想、正定蕴涵理想和蕴涵理想等概念在L~*-格值谓词演算下给予了新的刻画,讨论了它们的性质及其关系,研究了这些理想与其同态象、同态原象之间关系,获得了同类理想之积仍为该类理想.     

Primitive complete normal bases: Existence in certain 2-power extensions and lower bounds

The present paper is a continuation of the author’s work (Hachenberger (2001) [3]) on primitivity and complete normality. For certain 2-power extensions E over a Galois field F_q, we are going to establish the existence of a primitive element which simultaneously generates a normal basis over every intermediate field of E/F_q. The main result is as follows: Letq≡3mod4and letm(q)≥3be the largest integer such that2^m(q)dividesq²−1; ifE=F_q^2l, wherel≥m(q)+3, then there exists a primitive element inEthat is completely normal overF_q.Our method not only shows existence but also gives a fairly large lower bound on the number of primitive completely normal elements. In the above case this number is at least 4⋅(q−1)^2l−2. We are further going to discuss lower bounds on the number of such elements in r-power extensions, where r=2 and q≡1mod4, or where r is an odd prime, or where r is equal to the characteristic of the underlying field.     

Generic Splitting Fields of Central Simple Algebras: Galois Cohomology and Nonexcellence

A field extension L / F is called excellent if, for any quadratic form over F, the anisotropic part (L)an of over L is defined over F; L / F is called universally excellent if L E / E is excellent for any field extension E / F. We study the excellence property for a generic splitting field of a central simple F-algebra. In particular, we show that it is universally excellent if and only if the Schur index of the algebra is not divisible by 4. We begin by studying the torsion in the second Chow group of products of Severi–Brauer varieties and its relationship with the relative Galois cohomology group H3(L / F) for a generic (common) splitting field L of the corresponding central simple F-algebras.