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1.
Consider the stable Steinberg group St(K) over a skew field K. An element x is called an involution if x2 = 1. In this paper, an involution is allowed to be the identity. The authors prove that an element A of GLn(K) up to conjugation can be represented as BC, where B is lower triangular and C is simultaneously upper triangular. Furthermore, B and C can be chosen so that the elements in the main diagonal of B areβ1,β2, ...,βn, and of C areγ1,γ2,... ,γnCn, where cn∈[K*, K*] and = det A. It is also proved that every element 6 in St(K) is a product of 10 involutions.  相似文献
2.
For a finite commutative ring R and a positive integer k ? 2, we construct an iteration digraph G(R, k) whose vertex set is R and for which there is a directed edge from aR to bR if b = a k . Let R = R 1 ⊕ … ⊕ R s , where s > 1 and R i is a finite commutative local ring for i ∈ {1, …, s}. Let N be a subset of {R 1, …, R s } (it is possible that N is the empty set \(\not 0\) ). We define the fundamental constituents G N * (R, k) of G(R, k) induced by the vertices which are of the form {(a 1, …, a s ) ∈ R: a i D(R i ) if R i N, otherwise a i ∈ U(R i ), i = 1, …, s}, where U(R) denotes the unit group of R and D(R) denotes the zero-divisor set of R. We investigate the structure of G* N (R, k) and state some conditions for the trees attached to cycle vertices in distinct fundamental constituents to be isomorphic.  相似文献
3.
4.
The paper provides the construction of error-correcting pooling designs with the incidence matrix of two types of subspaces of symplectic spaces over finite fields. As a generalization of Guo et al.’s matrix, we use the general subspaces of type $(m,s)$ to substitute special subspaces of type $(2s,s)$ . If $\nu $ is big enough, we can get the higher degree of error-tolerant property.  相似文献
5.
Let G be a finite nonabelian group, ℤG its associated integral group ring, and Δ(G) its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups Q n (G) = Δ n (G)/Δ n+1(G) is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.  相似文献
6.
Let ? n [i] be the ring of Gaussian integers modulo n. We construct for ?n[i] a cubic mapping graph Γ(n) whose vertex set is all the elements of ?n[i] and for which there is a directed edge from a ∈ ?n[i] to b ∈ ?n[i] if b = a 3. This article investigates in detail the structure of Γ(n). We give suffcient and necessary conditions for the existence of cycles with length t. The number of t-cycles in Γ1(n) is obtained and we also examine when a vertex lies on a t-cycle of Γ2(n), where Γ1(n) is induced by all the units of ?n[i] while Γ2(n) is induced by all the zero-divisors of ?n[i]. In addition, formulas on the heights of components and vertices in Γ(n) are presented.  相似文献
7.
Hom-Malcev superalgebras can be considered as a deformation of Malcev superalgebras. We give the definition of Hom-Malcev superalgebras. Moreover, we characterize the Hom-Malcev operator and the representation of Hom-Malcev superalgebras. Finally, we study the central extension and the double extension of Hom-Malcev superalgebras.  相似文献
8.
Let \mathbbZpm \mathbb{Z}_{p^m } be the ring of integers modulo p m , where p is a prime and m ⩾ 1. The general linear group GL n ( \mathbbZpm \mathbb{Z}_{p^m } ) acts naturally on the polynomial algebra A n := \mathbbZpm \mathbb{Z}_{p^m } [x 1, …, x n ]. Denote by AnGL2 (\mathbbZpm ) A_n^{GL_2 (\mathbb{Z}_{p^m } )} the corresponding ring of invariants. The purpose of the present paper is to calculate this invariant ring. Our results also generalize the classical Dickson’s theorem.  相似文献
9.
在本文中,我们引入了一类环FIC环用于研究环的拟零因子图. 令$R$是一个环. 环$R$的拟零因子图,记为$\Gamma_*(R)$, 是一个定义在$R$的非零拟零因子上的有向图,图中的顶点$x$到另一个顶点$y$有一条边当且仅当$xRy=0$. 我们证明了下面三个条件等价: (1) $\chi(R)$是有限的; (2) $\omega(R)$是有限的; (3) $R$的素理想的有限交$\text{Nil}_*(R)$是有限的. 此外,我们还完全决定了图$\Gamma_*(R)$的连通性,直径,围长.  相似文献
10.
设$\mathbb{F}$是特征零代数闭域, $L$是域$\mathbb{F}$上除$A(n; n)$之外的基本典型李超代数. 本文证明了$L$上2-局部超导子是超导子,并且以spl(2; 2)的一个子代数为例说明存在2局部超导子不是超导子.  相似文献
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