广义中心α-Armendariz环

本文引入广义中心α-Armendariz环的概念,得到了广义中心α-Armendariz环的基本性质,研究了广义中心α-Armendariz环与其他环之间的一些关系.     

广义Hopf交叉余积

本文定义了一种广义的Hopf交叉余积,并证明了它等价于广义的cleft余扩张,也等价于具有余正规基的广义Galois余扩张.     

广义Hopf交叉余积

本文定义了一种广义的Hopf交叉余积,并证明了它等价于广义的cleft余扩张,也等价于具有余正规基的广义Galois余扩张.     

流形上广义扩张自映射

本文将紧流形上的扩张自映射推广到广义的扩张自映射.一方面,广义扩张自映射的一系列动态性质与扩张自映射的表现类似,参考文 M.Shub[3],并且任何扩张自映射在一定的 Riemann 度量下均可成为广义扩张自映射.另一方面,在这两类自映射之间存在着一个重要的差别,这就是扩张自映射是结构稳定的,而广义扩张自映射可以不是.本文所有的术语均可在文 S.Smale[4]中找到.     

环范畴和广义Г-环范畴间的关系

以R表示具有乘法单位元的结合环范畴,这里obR是结合环类,态射是保持单位元的环同态。以GΓR表示具有乘法单位元的广义Γ-环范畴,这里obGΓR是广义Γ-环类,态射是保持单位元的广义Γ-环同态。本文证明了:R和GΓR是等价的。     

环Z/pkZ上s次幂等矩阵及矩阵的加权广义逆

设R=Z/pkZ是模pk的有限局部环,其中p是素数,k>1,p≠2.本文确定了R上n阶s(s≥3)次幂等矩阵的伪标准形,得到了R上n阶矩阵A的加权{ , }-广义逆矩阵的计数定理.     

广义Goppa码最小距离下限的扩张及其译码

本文建立了由Lagrange插值公式决定的广义Goppa码最小距离下限扩张的一般定理,它包括了BCH码、广义BCH码和修改RS码的子域子码最小距离下限扩张结果,并对这些结果进行了改进,使其适用性更强.另外,本文还建立了用解线性方程组的方法实现最小距离下限扩张了的广义Goppa码的译码.广义Goppa码是目前较大的一种分组纠错码.因而,本文的结果可应用于现有的所有分组纠错码.     

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.     

广义完全极小集及其应用

定义了广义完全极小集,并证明了L为广义完全分配格与它的每个元都有广义完全极小集等价。在广义完全分配格中,给出了保广义完全极小集映射的几个等价刻画,并且在此基础上得到了广义完全分配格上的两个相应扩张定理。     

广义幂级数环的本质理想和非奇异性

本文研究了广义幂级数环与其系数环在本质理想和非奇异性上的关系.利用本质理想的定义和性质,得到了广义幂级数环的左理想为本质左理想的菪干充分必要条件.在此基础上,给出了广义幂级数环为左非奇异环的充分必要条件.     

半素环的(1,σ)导子扩张

本文给出了半素环的自同构和（ １,σ）导子的扩张命题,这推广了［１］中的一些结论,然后借助半素环的广义中心里的幂等元在（１,σ）导子扩张模上建立起拓扑空间,从拓扑学角度给出（１,σ）导子扩张模的结构定理．     

On Centroid and Extended Centroid of Rings

Abstract

We apply a notion of extended centroid to the whole class of nonassociative rings. We investigate the relation between the centroid and the extended centroid of a nonassociative ring.     

Center,Centroid, Extended Centroid,and Quotients of Jordan Systems

In this article we prove that the extended centroid of a nondegenerate Jordan system is isomorphic to the centroid (and to the center in the case of Jordan algebras) of its maximal Martindale-like system of quotients with respect to the filter of all essential ideals.     

Computing the extended centroid of abelian—group graded rings

We compute the extended centroid of a prime ring graded by an abelian group.     

The centroid of extended affine and root graded Lie algebras

We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.     

Primitive ideals of algebras

We prove the equivalence of two of Dixmier's conditions on primitive ideals, in a general ring-theoretic setting, and show that they are equivalent to a condition on the extended centroid.     

The Orlicz centroid inequality for star bodies

Lutwak, Yang and Zhang established the Orlicz centroid inequality for convex bodies and conjectured that their inequality can be extended to star bodies. In this paper, we confirm this conjecture.     

On Lie Ideals and Automorphisms in Prime Rings

Mathematical Notes - Let R be a prime ring of characteristic different from 2 with center Z and extended centroid C, and let L be a Lie ideal of R. Consider two nontrivial automorphisms α and...     

The Shephard type problems and monotonicity for L p -mixed centroid body

Lutwak and Zhang proposed the notion of L _p -centroid body. Further, Ma gave the definition of L _p -mixed centroid body, and obtained affirmative form for the Shephard type problems of L _p -mixed centroid body. In this article, we first give another affirmative form of the Shephard type problems for L _p -mixed centroid body, meanwhile, obtain its negative form. Next, we also give an extension of the generalized Funk’s section theorem for L _p -mixed centroid body. Finally, we establish two monotonicity inequalities of L _p -mixed centroid body.     

A Characterization of π-Complemented Algebras

π-complemented algebras are defined as those algebras (not necessarily associative or unital) such that each annihilator ideal is complemented by other annihilator ideal. Let A be a semiprime algebra. We prove that A is π-complemented if, and only if, every idempotent in the extended centroid of A lies in the centroid of A. We also show the existence of a smallest π-complemented subalgebra of the central closure of A containing A. In the case that A is a C*-algebra, this subalgebra turns out to be a norm dense *-subalgebra of the bounded central closure of A. It follows that a C*-algebra is boundedly centrally closed if, and only if, it is π-complemented.