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GCD整环与自反模 总被引:3,自引:0,他引:3
王芳贵 《数学年刊A辑(中文版)》1994,(2)
本文证明了凝聚整环是GCD整环当且仅当秩为1的自反模是自由模.同时还得到有限弱整体维数的凝聚整环是GCD整环当且仅当Pic(R)=1.特别地,有限整体维数的Noether整环是UFD当且仅当Pic(R)=1. 相似文献
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一个模嵌入自由模相当于用坐标来表示元素,这在数学上一直有重要意义.理论上, QF-环上的模都可以嵌入自由模,但没有好的算法,影响了它的应用.本文给出QF-环上有限生成模的最小嵌入的一种算法和所嵌入自由模的秩数的估计. 相似文献
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量子群的基变换与范畴同构 总被引:5,自引:1,他引:5
令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子群, A-Γ是环同态, Uг=UAΓ[Uг]是Uг的量子坐标代数,本文建立了量子坐标代数的基变换:即在相关约束条件下有Г-Hopf同构 A[U]AГ≌Г[Uг].我们证明了有限秩 A自由 1型可积 U模范畴和有限秩 A自由 A[U]余模范畴是同构的.特别,当 Г是域时,局部有限 1型 Uг模范畴和Г[Uг]余模范畴是同构的.最后,我们还证明了在[1]中定义的诱导函子和B.Parshall与王建磐博士在[2]中研究的诱导函子的一致性. 相似文献
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本文利用[1]中建立的关系,给出了半素右Noethcr环上所有加性秩函数对应的Gabriel拓朴与相应商环的构造,并建立了一般Noether环上加性秩函数与Artin环上模范畴中的有限长之间的联系. 相似文献
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设A_n(R)是有限局部环Z/p~k Z上n阶对称矩阵的集合,这里n≥2.p是大于2素数,p≡1(mod4)且k>1.通过确定有限局部环Z/p~k Z上对称矩阵的标准型,计算出A_n(R)在线性群GL_n(R)作用下的轨道数,从而计算出由特定对称矩阵确定的正交群的阶以及与特定对称矩阵在同一轨道的对称矩阵的阶. 相似文献
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In the study of symmetry classes of tensors, finding examples of symmetry classes of tensors that possess an o*-basis is of considerable interest. There are only few classes of groups that have been provided a necessary and sufficient condition for having such a basis. There is no general criterion for any finite group yet. In this note, we provide a necessary and sufficient condition for the existence of o*-basis of symmetry classes of tensors associated with semi-direct product of some finite abelian groups and, consequently, their wreath product. 相似文献
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A necessary and sufficient condition for the existence of orthogonal basis of decomposable symmetrized tensors for the symmetry classes of tensors associated with the dicyclic group is given. In particular we apply these conditions to the generalized quaternion group, for which the dimensions of the symmetry classes of tensors are computed. 相似文献
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On the orthogonal basis of the symmetry classes of tensors associated with the dicyclic group 总被引:1,自引:0,他引:1
A necessary and sufficient condition for the existence of orthogonal basis of decomposable symmetrized tensors for the symmetry classes of tensors associated with the dicyclic group is given. In particular we apply these conditions to the generalized quaternion group, for which the dimensions of the symmetry classes of tensors are computed. 相似文献
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设V是一个n维线性空间,V_x~m(G)为V上的张量对称类.A为V的线性算子T的矩阵,K(A)为V_x~m(G)上的诱导线性算子K(T)的矩阵.本文从K(A)的数值半径Υ(K(A))和可分数值半径Υ_x(K(A))定义出发,研究了Υ(K(A))、Υ_x(K(A))与范数||A||_p(1≤p≤2)、广义矩阵函数d_x~G(A)的关系,得到了它们之间的两个不等式. 相似文献
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In this article necessary and sufficient conditions are given for the existence of an orthogonal basis consisting of standard (decomposable) symmetrized tensors for the class of tensors symmetrized using a Brauer character of the dihedral group. 相似文献
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M. R. Pournaki 《Southeast Asian Bulletin of Mathematics》2002,25(3):523-527
Let G be a finite group and a set of n elements. Assume that G acts faithfully on and let V be a vector space over the complex field , with dim V = m 2. It is shown that for each irreducible constituent of permutation character of G, the symmetry class of tensors associated with G and is non-trivial. This extends a result of Merris and Rashid (see [6, Theorem 2]).1995 AMS subject classification
primary 20C30 secondary 15A69This research was in part supported by a grant from IPM. 相似文献
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We present a method for constructing an orthonormal basis for a symmetry class of tensors from an orthonormal basis of the underlying vector space. The basis so obtained is not composed of decomposable symmetrized tensors. Indeed, we show that, for symmetry classes of tensors whose associated character has degree higher than one, it is impossible to construct an orthogonal basis of decomposable symmetrized tensors from any basis of the underlying vector space. We end with an open problem on the possibility of a symmetry class having an orthonormal basis of decomposable symmetrized tensors. 相似文献
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We present here the dimensions of some subspaces in the symmetry classes of tensors and some methods for constructing orthonormal bases of the symmetry classes of tensors. 相似文献
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Symmetry classes of tensors associated with certain groups 总被引:1,自引:0,他引:1
We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with certain subgroups of the full symmetric group The dimensions of these symmetry classes of tensors are also given 相似文献