共查询到18条相似文献,搜索用时 140 毫秒
1.
半群O_n(k)的秩 总被引:1,自引:1,他引:0
设O_n是有限链[n]上的保序变换半群.对任意1≤k≤n-1,研究半群O_n(k)={α∈O_n:(x∈[n]x≤k→xα≤k}的秩和幂等元秩,证明了半群O_n(k)的秩为2n-3.进一步,得到了半群O_n(k)(2≤k≤n-1)的幂等元秩为n和半群O_n(1)的幂等元秩为n-1. 相似文献
2.
保持矩阵迹的乘法映射 总被引:5,自引:0,他引:5
设F是一个域 ,An,是一个乘法半群且满足 {aEij|i,j=1 ,2… ,n ,a∈F} An (F) ,其中Mn(F)定义F上所有n×n矩阵组成的乘法半群 ,本文证明了一个结果 :若f:AnF是一个保迹映射 ,则存在一个可逆阵P∈Mn(F)使得f(A) =PAP- 1 , A∈An由此推广了 [1 ]的一个结果 . 相似文献
3.
1.引言 我们讨论下列广义特征值反问题: (G)已知B是n×n阶对称半正定矩阵,λ=(λ_1,…,λ_(2n-1))~T∈R~(2n-1),且{λ_i}~(n_3),和{λ_i}_(n+1)~(2n-1)严格交错。问题是欲求一个实对称三对角n×n阶矩阵A,使得λ_1…,λ_n是Ax=λBx的特征值,λ_(n+1),…,λ_(2n-1)是A_(n-1)x=λB_(n-1)x的特征值,其中A_(n-1),B_(n-1)分别是矩阵A,B的前n-1阶主子阵。 相似文献
4.
《数学的实践与认识》2015,(10)
压缩变换半群CT_n是全变换半群T_n中的压缩元组成的子半群.主要讨论了当n≥5时CT_n中一类元素{α∈CT_n|1α=1,((n-2)α,(n-1)α,nα)=(3,2,1))的基数并得到了递推公式:LN_n~((1,321))=d-d_1LN_(n-1)~(((1,321))-…-d_(k-3)LN_(n-(k-3))~((1,321)). 相似文献
5.
6.
r—不可分矩阵的本原指数 总被引:2,自引:1,他引:1
周积团 《数学的实践与认识》2003,33(5):96-98
本文给出了 n阶 r—不可分矩阵的本原指数的上界 ,即 n阶 r—不可分矩阵的本原指数 ( A)≤ n-r( 1≤ r2 ,都能找到一类本原指数为 n-1的 n阶 1—不可分矩阵 .证明了 n阶 1—不可分矩阵的本原指数集 En={ 1 ,2 ,… ,wn} ( wn=n-1 ) . 相似文献
7.
设Sing_n是[n]上的奇异变换半群.证明了半群Sing_n是由秩为n-1的非群平方幂等元生成的,且它的非群平方幂等元秩为(n(n-1))/2. 相似文献
8.
OI_n的理想K(n,r)的极大逆子半群 总被引:3,自引:0,他引:3
Xn为n元有限集,OIn为Xn上的一切保序严格部分一一变换半群.记K(n,r)={α∈OIn∶|Tmα|≤r}(0≤r≤n-1)则K(n,r)(0≤r≤n-1)是OIn的理想.我们刻划了K(n,r)(1≤r≤n-1)的极大逆子半群. 相似文献
9.
本文给出了 n阶 r-不可分矩阵的本原指数的上界 ,即任 n阶 r—不可分矩阵 A的本原指数 (A)≤n+(r- ) 2r (1≤ r相似文献
10.
设自然数n≥5,X_n={1,2,…,n},并赋予自然数的大小顺序,令H(SPO_n,r)=SPO_n∪L(n,r)(5≤n,2≤r≤n-3)是X_n上的全相似部分保序变换半群.得到全相似保序变换半群H(SPO_n,r)的秩为■. 相似文献
11.
Yi-jia Tan 《Semigroup Forum》2006,73(1):31-44
In this paper, the concepts of primitive matrices over a distributive lattice L are introduced, and some algebraic properties
of primitive circulant matrices over the lattice L are obtained. Also, some characterizations of the set of all primitive
circulant
matrices over the lattice L of order n as a semigroup are given. 相似文献
12.
设OI_n是[n]上的保序严格部分一一变换半群.对任意1≤k≤n-1,研究半群OI_n(k)={α∈OI_n:(■x∈dom(α))x≤k■xα≤k}的秩,证明了半群OI_n(k)的秩为n+1. 相似文献
13.
设X_n={1,2,…,n}并赋予自然数序,MCK_n是X_n上核具有连续横截面保序或反序变换所构成的半群.K_n是MCK_n的最大正则子半群.本文将考虑K_n的理想K(n,r)={α∈K_n:|im(α)|≤r}(3≤r≤n-1).证明了K(n,r)的秩为(n-r+1)(n-r+2)(n-r+3)/6. 相似文献
14.
The Semigroup of Hall Matrices over Distributive Lattices 总被引:3,自引:0,他引:3
Yijia Tan 《Semigroup Forum》2000,61(2):303-314
In this paper, the semigroup Hn (L) of Hall matrices over a complete and completely distributive lattice L is studied. A Hall matrix is a matrix which is greater (for the order associated with the lattice structure) than an invertible matrix. Some necessary and sufficient conditions for a Hall matrix to be regular in the semigroup Hn (L) are given and Green's relations of the semigroup Hn (L) are described. Also, the sandwich semigroup of Hall matrices over the lattice L is studied. 相似文献
15.
Yi-jia Tan 《Southeast Asian Bulletin of Mathematics》2000,24(3):475-479
Let Cn(L) denote the set of all n × n circulant matrices over a distributive lattice L. Then Cn(L) forms a semigroup under the usual matrix product. In this paper, we shall characterize all idempotents in Cn(L), and also estabish the Euler-Fermat theorem for the semigroup Cn(L).AMS Subject Classification (2000): 20MSupported by the Educational Committee of Fujian, China. 相似文献
16.
Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn(F) be the multiplicative semigroup of all n × n matrices over F, and let M^Pn(F) be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn(F) such that F M^Pn(F). A map f : F→R is called a homomorphism if f(AB) = f(A)f(B) for any A, B ∈F. In particular, f is called an endomorphism if F = R. The structure of all homomorphisms from F to R (respectively, all endomorphisms of Mn(F)) is described. 相似文献
17.
主要目的是利用初等方法研究LCM序列和SLOS数列的性质,并给出一个包含这两个数列的恒等式及渐近公式.结论:证明了L(2n)L(n)=SLO2S.S L2OnS(+22n 1--1)1和ln(L(n))=n+O n exp-(l nc(lnln n n))5153. 相似文献
18.
A filter in a semigroup is a subsemigroup whose complement is an ideal. (Alternatively, in a quasiordered semigroup, a slightly more general definition can be given.) We prove a number of results related to filters in a semigroup and the lattice of filters of a semigroup. For instance, we prove that every complete algebraic lattice can be the lattice of filters of a semigroup. We prove that every finite semigroup is a homomorphic image of a finite semigroup whose lattice of filters is boolean and which belongs to the pseudovariety generated by the original semigroup. We describe filter lattices of some well-known semigroups such as full transformation semigroups of finite sets (which are three-element chains) and free semigroups (which are boolean). 相似文献