Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two

Let be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity ((((x ₁,x ₂),x ₃), ((x ₄,x ₅),x ₆)), (x ₇,x ₈)) = 0 (((x ₁ x ₂ · x ₃)(x ₄ x ₅ · x ₆))(x ₇ x ₈) = 0, respectively). In this paper, we construct infinite independent systems of identities in the variety ( , respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety has the cardinality of the continuum and that there are algebras in with undecidable word problem.     

关于有限域F_q上矩阵阶的研究

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     

Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two

Let X_n denote the set of quadratic forms in n variables over a finite field F_q of characteristic 2, and X_n the association scheme on X_n by defining the relations with respect to the type of quadratic forms. We prove that every automorphism of X_n is of the form X P^tXP + Y for all X X_n, where P GL_n(F_q), is an automorphism of F_q, and Y X_n.2000 Mathematics Subject Classification: 05E30Supported by the National Natural Science Foundation of China (10271039), Hobei Natural Science Foundation (102132) and Hebei Education Committee.     

The Identities and the Central Polynomials of the Infinite Dimensional Unitary Grassmann Algebra Over a Finite Field

We describe the T-ideal of identities and the T-space of central polynomials for the infinite dimensional unitary Grassmann algebra over a finite field.     

有限维中心代数上矩阵方程组的广对称解与斜广对称解

设Ω是一个具有对合反自同构的有限维中心代数且charΩ≠2.本文在Ω上定义了广对称矩阵和斜广对称矩阵,在Ω[λ]上考虑了三个矩阵方程组,分别给出了其有广对称解和斜广对称的充要条件.作为特例,得到了某些矩阵方程相应的结果.     

有限域上遍历矩阵的特性研究

对有限域上遍历矩阵的性质进行了分析,给出了有限域上遍历矩阵的计数定理,并对遍历矩阵序对(A,B)关于矩阵M的双侧幂乘集〈A〉M〈B〉的秩及基数进行了全面分析.给出了R_k(A,B)集的构成及其基数的有关定理,所得到的结论对利用遍历矩阵实现有关的公钥密码具有理论上的指导意义.     

Correction to: Involutions of Type G2 over a Field of Characteristic Two

Algebras and Representation Theory - We would like to correct two errors in our paper Involutions of type G2 over a field of characteristic 2 [2].     

有限集合上偏序关系的矩阵判别方法

要从定义出发去判断集合X上的二元关系R是否是偏序关系比较困难,从关系矩阵出发,给出了偏序关系的矩阵判别方法,并对此方法进行了证明.     

关于广义四元数代数上矩阵的迹的一个等式

众所周知,相似矩阵的迹相等对于非交换代数和环上的矩阵不一定成立,有趣的问题是给定一个条件使得相似矩阵的迹相等对于非交换代数或非交换环上的矩阵成立。本文对于特征不是2的任意域F上定义的广义四元数代数上的两个矩阵A和B,给出如果A和B相似并且它们的主对角线上的元素在F中,那么它们的迹相等。     

Diophantine Undecidability of Function Fields of Characteristic Greater than 2, Finitely Generated over Fields Algebraic over a Finite Field

Let F be a function field of characteristic p > 2, finitely generated over a field C algebraic over a finite field C _p and such that it has an extension of degree p. Then Hilbert's Tenth Problem is not decidable over F.     

Matrices which Commute with their Transposes over a Field of Characteristic Two

Let M be a square matrix with entries in a field F of characteristic two. I show that a necessary and sufficient condition for M to be similar to a matrix over F which commutes with its transpose is that one of the following statements holds.

i) The minimal polynomial of M is not square-free.

ii) Some elementary divisor of M occurs with multiplicity greater than or equal to its degree of inseparability.     

Classification of Finite Factor Representations of the (2m+1)-Dimensional Heisenberg Group over a Countable Field of Finite Characteristic

For a field F that is the direct limit of an increasing chain of finite fields, we describe the Bratteli diagram, the finite complex factor representations, the Plancherel formula, and the projective modules of the corresponding Heisenberg group.     

特征2的有限域上二次型间的表示个数

本文利用特征2有限域Fq上奇异正交几何理论给出Fq上二次型的型与型间具有秩k的表示的个数,并由此得到一般计数公式及其q超几何级数表达式.     

完全不确定Hamburger矩阵矩量问题的有限阶解

该文描述带有矩量序列{v_m}_0~∞■C~(q×q)的完全不确定Hamburger矩阵矩量问题:v_m=integral from n=-∞to∞x~m dρ(x),m=0,1,…的有限阶解,即该问题的那些解ρ,使得C~(q×q)-值多项式的线性空间P在对应的空间L~2(R,dρ/E(x))内稠密,这里E(x)为在实轴R上取正值的某个数值多项式.作为预备知识,作者考虑所谓广义Akhiezer插值的矩阵变种与它的相关矩阵矩量问题之间的一种关系.     

除环上矩阵的子矩阵的秩的恒等式与不等式

本文提供了除环上矩阵的一些子矩阵的秩的若干恒等式与不等式,出现在本文中的这些结果,在处理涉及某些应用方面的复矩阵(作为除环上矩阵的特例)问题以及某些纯数学问题将起重要作用。     

The Group Ring of SL2(p) over p-adic Integers for p Odd

Let p > 2 be a prime, R =  _p[ζ_p^f − 1], K =  _p[ζ_p^f − 1], and G = SL₂(p^f). The group ring RG is calculated nearly up to Morita equivalence: The projections of RG into the simple components of KG are given explicitly and the endomorphism rings and homomorphism bimodules between the projective indecomposable RG-lattices are described.     

交换半环上三角矩阵代数的Jordan同构

探讨交换半环上的上三角矩阵代数的Jordan同构.证明如果R是一个交换半环且R中仅有幂等元0与1,那么从R上的上三角矩阵代数Tn(R)到R上的任意代数的每一个Jordan同构要么是一个同构要么是一个反同构.     

Characterization of 2-Pisot Elements in the Field of Laurent Series over a Finite Field

Mathematical Notes - Let Fq be a finite field, and let Fq[X] be the ring of polynomials with coefficients in Fq. A 2-Pisot element is a pair of algebraic integers of formal Laurent series over...     

The Identities and Central Polynomials of the Finite Dimensional Unitary Grassmann Algebras Over a Finite Field

We describe the T-ideal of identities and the T-space of central polynomials for the unitary finite dimensional Grassmann algebra over a finite field.