Pseudopolarity of Generalized Matrix Rings over a Local Ring

Pseudopolar rings are closely related to strongly -regular rings, uniquelystrongly clean rings and semiregular rings. In this paper, we investigate pseudopolar-ity of generalized matrix rings Ks（R） over a local ring R. We determine the conditionsunder which elements of Ks（R） are pseudopolar. Assume that R is a local ring. It isshown that A ∈ Ks（R） is pseudopolar if and only if A is invertible or A^2 ∈ J（Ks（R））or A is similar to a diagonal matrix [ u 0 0 j ]; where lu -rj and lj-ru are injectiveand u 2 U（R） and j ∈ J（R）. Furthermore, several equivalent conditions for Ks（R）over a local ring R to be pseudopolar are obtained.

Using Normal Form of Idempotent Matrices over Finite Local Ring Z/p^kZ to Construct Cartesian Authentication Codes

In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.

基于Ring-Sum-Expansion范式的Reed-Muller展开式算法

为了改善生成Reed-Muller展开式的灵活性,提出了基于RSE范式的Reed-Muller展开式算法.根据将析取主范式转化为Ring-Sum-Expansion范式的过程,先使用真值表输入项构造预处理表,再从真值表中抽取使输出项为真的二进制码,通过预处理表直接解出每一个输出项的Reed-Muller展开式.对算法进行复杂度分析比较表明,与通常所用的GRM递归算法和GRM矩阵相乘Reed-Muller展开式算法相比,该算法在生成展开式时具有更好的灵活性,可以单独生成指定输出项的Reed-Muller展开式,不同于常用算法必须要一次生成全部输出项的Reed-Muller展开式.

J-clean and Strongly J-clean Rings

Let R be a ring and J（R） the Jacobson radical. An element a of R is called（strongly） J-clean if there is an idempotent e ∈ R and w ∈ J（R） such that a = e ＋ w（and ew = we）. The ring R is called a（strongly） J-clean ring provided that every one of its elements is（strongly） J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.

Triangular Matrix Representations of Rings of Generalized Power Series

Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].

On Realization of Fusion Rings from Generalized Cartan Matrices

The Casimir element of a fusion ring （R, B） gives rise to the so called Casimir matrix C of （R,B）. This enables us to construct a generalized Cartan matrix D - C in the sense of Kac for a suitable diagonal matrix D. In this paper, we study some elementary properties of the Casimir matrix C and use them to realize certain fusion rings from the generalized Cartan matrix D - C of finite （resp. affine） type. It turns out that there exists a fusion ring with D - C being of finite （resp. affine） type if and only if D - C has only the form A2 （resp. A1^（1）））. We also realize all fusion rings with D - C being a particular generalized Cartan matrix of indefinite type.

A Class of Maximal General Armendariz Subrings of Matrix Rings

An associative ring with identity R is called Armendariz if, whenever （∑^m i=0^aix^i）（∑^n j=0^bjx^j）=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring （with or without identity） and a general Armendariz ring （with or without identity）, and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings.

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.

基于计算机图像处理技术的皮革表面缺陷检测研究现状及展望

皮革表面缺陷的检测对皮革制品的生产销售具有重要的影响。本文立足现有研究资料,汇总介绍了目前计算机图像处理技术在皮革表面缺陷检测中的流程及常用方法,发现计算机图像处理技术虽然能够提升皮革表面缺陷检测的速度,但其准确度及稳定性仍存在较大的改进空间,需加以完善。

形式三角矩阵半环的广义导子

半环理论是代数理论上研究的热点问题。近年来,越来越多的研究人员注意到了半环理论在数学及其他研究领域的运用也非常普遍,在这些其他学科中有着广泛的应用。研究了形式三角矩阵半环Tri(A,M,B)上的广义导子的定义和表示形式。给出了半环上双半模上的拟同态映射f的定义。证明了半环Tri(A,M,B)上的任意的一个广义导子可以由半环A,B上的广义导子和(A,B)-双半模M上的一个拟同态映射来表示。

局部环上的三阶J-拟polar矩阵

基于群自同构及矩阵的相关性质,研究了三阶矩阵环的两类特殊子环L(R)与S(R)的J-拟polar性,给出了在局部环条件下上述两类矩阵环为J-拟polar环的充分必要条件,证明了若R是局部环,则L(R)是J-拟polar环当且仅当S(R)是J-拟polar环当且仅当R是UB-环且R/J(R)■2.

Differential Inverse Power Series Rings with Quasi-Armendariz-like Condition

A generalization of semiprime rings and right p.q.-Baer rings,which we call quasi-Armendariz rings of differential inverse power series type(or simply,DTPS-quasi-Armendariz),is introduced and studied.It is shown that the DTPS-quasi-Armendariz rings are closed under direct sums,upper triangular matrix rings,full matrix rings and Morita invariance.Various classes of non-semiprime DTPS-quasi-Armendariz rings are provided,and a number of properties of this generalization are established.Some characterizations for the differential inverse power series ring R[[x^-1;δ]]to be quasi-Baer,generalized quasi-Baer,primary,nilary,reflexive,ideal-symmetric and left AIP are conncluded,whereδis a derivation on the ring R.Finally,miscellaneous examples to illustrate and delimit the theory are given.

Notes on Rings with Strong 2-Sum Property

A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to have the strong 2-sum property.

Structure of Zhou Nil-clean Rings

戒指 R 是周无干净如果在 R 的每个元素是变换的二 tripotents 和 nilpotent 的和。周的同构的图象无干净的戒指被探索。如果并且仅当 30 R 是 nilpotent ， R/30R 是周，我们证明戒指 R 是周无干净无干净如果(R)是无并且仅当 R/BM (R)是5有势力和 BM ，如果(R)对一枚布尔戒指同形并且仅当 J (R)是无和 R/J ，一枚 Yaqub 戒指，一枚贝尔戒指或如此的戒指的一个直接产品。借助于同构的图象，我们完全决定概括矩阵戒指什么时候是周无干净。我们证明概括矩阵包围 Mn (R；s ) 是周无干净如果并且仅当 R 是无干净的周和 s J (R) 。

含分布式电源的环网故障定位的改进矩阵算法

为解决含高渗透率分布式电源DG(distributed generation)的配电环网对故障定位的要求,提出一种改进的故障定位矩阵算法。该算法以网络描述矩阵为基础,并利用馈线终端设备FTU(feeder terminal unit)收集上报的故障电流幅值信息形成改进的故障信息矩阵,通过由网络描述矩阵和故障信息矩阵运算后得到的故障判断矩阵可直接定位故障区域。该算法的优点有:计算量小,运算得出的故障判据简单直观,克服了传统矩阵算法中需根据不同电源假设不同的正方向的不足。对于含多个DG的环网,能在定义一次正方向的前提下准确定位出单一或多重故障,并给出了在故障信息不完备情况下的解决对策。最后通过仿真算例,验证了该算法的有效性。

局部环上n阶矩阵的{1}-逆作成的群

研究了有单位元的可换局部环上n阶可对角化的矩阵A的{1}-逆集中的子群及其构造问题,运用矩阵和群方法,给出了这个矩阵A的{1}-逆集AP{1}-中元素的乘法封闭的条件,获得了矩阵A的{1}-逆集AP{1}中的子集作成群的充要条件,以及这些子群的结构定理及相关结果.

环形振子径向矩阵元的通项表达式及其递推关系

利用文献 1给出的环形振子的归一化的径向波函数 ,推导出环形振子径向矩阵元的通项表达式及其递推关系 .解决了环形振子径向矩阵元的计算问题 .

可换环上上三角矩阵李代数的局部自同构和局部导子（英文）

本文刻画了Tn(R)上的局部自同构和局部导子.利用关于Tn(R)的自同构和导子的主要结果和矩阵计算技巧,本文证明了Tn(R)上的每一个局部自同构是自同构,每一个局部导子是导子,这推广了文献关于Tn(R)的自同构和导子的主要结果.

环Z/p^kZ上m阶交错矩阵的计数定理及其应用

设Wm(R)是有限局部环R =Z/pkZ上所有m阶交错矩阵所构成的集合(p是素数,k >1).该文通过确定R上任意m阶交错矩阵的标准形,计算出Wm(R)在线性群GLm(R)作用下的轨道数及n(2r,2t,r1, ,r1s1, ,rl, ,rlsl),其中 W(2r,2t,r1, ,r1s1, ,rl, ,rlsl)(∑li=1si =t) 表示不变因子为(2r,2t,r1, ,r1s1, ,rl, ,rlsl)的所有m阶交错矩阵构成的集合,n(2r,2t,(2r,2t,r1, ,r1s1, ,rl, ,rlsl)表示其中的元素个数.最后,作者利用有限局部环R上交错矩阵的标准形构作了一个Cartesian认证码。

Bezout domain环上矩阵的广义逆

给出了Bezoutdomain环上矩阵广义逆的定义,并利用Bezoutdomain环酉矩阵的概念得出A+存在的充要条件及(i,…,j)-逆的表达式,从而得到一些有意义的结果。