对称无限布尔方阵的本原指数的一个计算公式

引入了本原无限布尔方阵的概念,给出了对称无限布尔方阵为本原阵的一个充分必要条件,最后给出了对称本原无限布尔方阵的本原指数的一个计算公式.     

对称无限布尔方阵的本原指数集的刻划

研究了对称无限布尔方阵,给出了对称无限布尔方阵为本原阵的一个充分必要条件,证明了具有有限直径d的对称无限布尔方阵的本原指数的上确界为2d,最后证明了直径不超过d的全体对称本原无限布尔方阵的本原指数集是E_d={1,2,…,2d}.     

围长为2的本原无限布尔方阵类的本原指数集

研究了围长为2的无限布尔方阵的本原性,通过无限有向图D（A）的直径给出了这类矩阵的本原指数的上确界,最后证明了直径小于等于d且围长为2的本原无限布尔方阵所构成的矩阵类的本原指数集为Ed^0={2,3,…,3d}．     

具有有限周期的无限布尔方阵的传递指数

给出了无限布尔方阵周期的概念,研究了无限布尔方阵伴随有向图的若干性质,研究了有限布尔矩阵幂的图论性质,最后给出了无限布尔方阵传递指数的上、下界估计.     

n阶(n-1)-循环布尔矩阵的本原性及可约性的判定

以0,1为元素所构成的n阶方阵A=(a_(ij))_(n×n),i,j=0,1,2,…n-1,其元素之间的加法与乘法运算按下列方式:则称A为布尔矩阵,文[1],[2]对这类矩阵的性质作了深入的研究和全面的介绍,文[4][5]给出了经典循环矩阵可约性和本原性的条件,本文给出了另一类循环布尔矩阵的可约性和本原性的充分必要条件。设g是一个非负整数,一个n阶g-循环矩阵A_()=(a_(ij))_(n×n)是一个这样的矩阵,除     

本原环的无限Galois理论

本文首先建立了线性变换环,连续交换环及有非零基座的本原环与单纯Artin环的无限Galois理论是Galois等价的。然后建立了有非零基座的本原环的无限Galois理论。显然,线性变换完全环和连续变换环的无限 Galois理论是其特例。     

关于几乎可分方阵指数的一个猜想

在文[1]中,提出了n阶几乎可分布尔方阵A中1的个数σ(A)及其本原指数γ(A)之间关系的一个猜想.本文给出了一族反倒,证明了这一猜想对于n≥6的所有情形都是不成立的.     

几乎可分方阵类的本原指数集

本文刻划了n阶几乎可分方阵类的本原指数集以及一些极阵,并提出了一个有关的猜想.     

循环矩阵的两种特性的判定

揭示几类矩阵之间的紧密联系.借助于群的子群的判定以及循环布尔矩阵是本原矩阵的判定方法,得到循环模糊矩阵成为幂等矩阵的充要条件,反循环布尔矩阵成为本原矩阵的充要条件.并给出了循环模糊矩阵成为幂等矩阵的判定方法,反循环布尔矩阵成为本原矩阵的判定方法.     

关于拟本原环

本文在[1,2]基础上,对拟本原环给出了一个新的定义,并着重举出例子,说明在本文定义下的拟本原环,一般不再是通常的本原环,虽然通常的本原环必是拟本原环。此时,我们确信对本文所定义的拟本原环可建立文[1]中对本原环所有的定理。     

On the generalized indices of boolean matrices

We characterize completely those Boolean matrices with the largest generalized indices in the class of Boolean matrices and in the class of reducible Boolean matrices and derive a new upper bound for the generalized index in terms of period. We also generalize the upper and lower multiexponents of primitive Boolean matrices to general Boolean matrices.     

On the generalized indices of boolean matrices

We characterize completely those Boolean matrices with the largest generalized indices in the class of Boolean matrices and in the class of reducible Boolean matrices and derive a new upper bound for the generalized index in terms of period. We also generalize the upper and lower multiexponents of primitive Boolean matrices to general Boolean matrices.     

On the hall exponents of boolean matrices

We obtain upper bounds on the Hall exponents of symmetric and microsymmetric primitive Boolean matrices respectively.     

On the hall exponents of boolean matrices

We obtain upper bounds on the Hall exponents of symmetric and microsymmetric primitive Boolean matrices respectively.     

The Semigroup of Primitive Generalized Circulant Boolean Matrices

In this paper, the semigroup of primitive generalized circulant Boolean matrices is studied, and some algebraic properties of this semigroup are obtained. Also, an asymptotic formula for the cardinality of the semigroup is given.     

The primitive Boolean matrices with the second largest scrambling index by Boolean rank

The scrambling index of an n × n primitive Boolean matrix A is the smallest positive integer k such that A ^k (A ^T) ^k = J, where A ^T denotes the transpose of A and J denotes the n×n all ones matrix. For an m×n Boolean matrix M, its Boolean rank b(M) is the smallest positive integer b such that M = AB for some m × b Boolean matrix A and b×n Boolean matrix B. In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an n×n primitive matrix M in terms of its Boolean rank b(M), and they also characterized all primitive matrices that achieve the upper bound. In this paper, we characterize primitive Boolean matrices that achieve the second largest scrambling index in terms of their Boolean rank.     

On fully indecomposable exponent for primitive boolean matrices with symmetric ones

If A is a primitive matrix, then there is a smallest power of A (its fully indecomposable exponent) which is fully indecomposable, and a smallest power of A (its strict fully indecomposable exponent) starting from which all powers are fully indecomposable. We obtain bounds on these two exponents for primitive Boolean matrices with symmetric one's.