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Kirby C. Smith 《代数通讯》2013,41(6):2065-2077
Let R be a right near-ring with identity. The k×k matrix near-ring over R, Matk(R R), as defined by Meldrum and van der Walt, regards R as a left mod-ule over R. Let M be any faithful left R-module. Using the action of R on M, a generalized k×k matrix near-ring, Matk(R M), is defined. It is seen that Matk(R M) has many of the features of Matk(R R). Differences be-tween the two classes of near-rings are shown. In spe- cial cases there are relationships between Matk(R M) and Matk(R R). Generalized matrix near-rings Matk(R M) arise as the “right near-ring” of finite centraiizer near-rings of the form M A{G)> where G is a finite group and A is a fixed point free automorphism group on G. 相似文献
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Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG(H)={α ∈ RG|αh = hα for all h ∈ H), which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG(H) is just the central subalgebra Z(RG) of RG. In this note, we show that the set of all H- conjugacy class sums of G forms an R-basis of CRG(H). Furthermore, let N be a normal subgroup of G and γthe natural epimorphism from G to G to G/N. Then γ induces an epimorphism from RG to RG, also denoted by % We also show that if R is a field of characteristic zero, then γ induces an epimorphism from CRG(H) to CRG(H), that is, 7(CRG(H)) = CRG(H). 相似文献
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Zhengxing Li & Jinke Hai 《数学研究通讯:英文版》2011,27(3):227-233
Let $G$ be a finite group, $H ≤ G$ and $R$ be a commutative ring with
an identity $1_R$. Let $C_{RG}(H) = \{ α ∈ RG|αh= hα$ for all $h ∈ H \}$, which is called
the centralizer subalgebra of $H$ in $RG$. Obviously, if $H = G$ then $C_{RG}(H)$ is just
the central subalgebra $Z(RG)$ of $RG$. In this note, we show that the set of all $H$-conjugacy class sums of $G$ forms an $R$-basis of $C_{RG}(H)$. Furthermore, let $N$ be a
normal subgroup of $G$ and $γ$ the natural epimorphism from $G$ to $\overline{G}= G/N$. Then $γ$ induces an epimorphism from $RG$ to $R\overline{G}$, also denoted by $γ$. We also show that if $R$ is a field of characteristic zero, then $γ$ induces an epimorphism from $C_{RG}(H)$ to $C_{R\overline{G}}(\overline{H})$, that is, $γ(C_{RG}(H)) = C_{R\overline{G}}(\overline{H})$. 相似文献
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本文利用四元数矩阵方程AX-XB=C有唯一解的充要条件给出了两个定理,并讨论了特殊条件下四元矩阵方程AX-XB=C在C=0和C=0且A=B两种情况下解的性质. 相似文献
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In this paper, the authors study the Cohen-Fischman-Westreich''s
double centralizer theorem for triangular Hopf algebras in the
setting of almost-triangular Hopf algebras. 相似文献
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详细地研究了有限域 Fq上的矩阵的阶的问题 ,得到了相当理想的结果 .并给出一类矩阵方幂的极小多项式的求法 相似文献
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建立了复正定矩阵的几个行列式不等式,将正定Hermite阵的Minkowski不等式、 Ostrowski-Taussky不等式推广到了复正定矩阵上,推广改进了一些文献的结果. 相似文献
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设Ω是一个特征非2的具有对合反自同构的有限维中心代数.本文研究Ω上的两个矩阵方程组,分别给出了其有一般解和次(斜)自共轭解的充要条件. 相似文献
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广义四元数体上矩阵的最小多项式 总被引:15,自引:3,他引:15
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。 相似文献
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A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications 总被引:3,自引:0,他引:3
QingWenWANG 《数学学报(英文版)》2005,21(2):323-334
We consider the system of four linear matrix equations A1X = C1, XB2=C2, A3XB3=C3 and A4XB4 = C4 over h, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A1X = C1 and A3X=C3 to have a bisymmetric solution, the system of matrix equations A1X = C1 and A3XB3 = C3 to have a perselfconjugate solution over h with an involution and char h≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary resultson other systems over h are obtained. The previous known results on some systems of matrix equations are special cases of the new results. 相似文献
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任意体上的双矩阵分解与矩阵方程 总被引:15,自引:1,他引:14
本文给出了任意体上具有相同行数或相同列数的双矩阵分解定理;利用此定理,给出了任意体上的矩阵方程AXB+CYD=E及[A1XB1,A2XB2]=[E1;E2]有解的充要条件及其一般解的表达式. 相似文献
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,AFurtherStudyoftheSystemofMatrixEquationsoveraSkewField¥WangQingwen(Dept.ofMath.,ChangweiTeachersCollege,Weifang,261043)Wang?.. 相似文献
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中心代数上一矩阵方程的中心对称与中心斜对称解 总被引:2,自引:1,他引:1
Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered. 相似文献