关于循环环的诣零根与诣零理想的结构

研究了循环环R=(a²=ka,k≠0)的诣零根和诣零理想的结构,得到了如下主要结论:1)若|R|=∞,则K(R)={0},从而诣零理想只有{0}.2)若|R|=n>1,1≤k,其阶为n/μ(n,k);(2)R的所有诣零理想为{<λμ(n,k)a>,其中λ为n/μ(n,k)的正因数}.3)若|R|=n>1,1≤ki=1^s,其中p1,p2,…,Ps是整除n而不能整除k的全部互异素数.     

环上的线性群

<正> 体上线性群的自同构及构造曾有很详尽的研究(详见[1],[2]).整数环上线性群的自同构是由华罗庚及 I.Reiner 开始研究的.万哲先及了 J.Landin 和 I.Riener 讨论了非交换主理想整环上一般线性群的自同构,[4]中还讨论了非交换欧氏环上特殊线性群的自同构.本文将讨论一般环上线性群的自同构与构造.以 R 表任一给定的环,R 上的 n 级特殊线性群 SL_n(R)定义为由一切形如(?)(其中 I=I~((n)),是 n 阶单位方阵,Eij 表示在(i,j)位置上有元素1而其余位置是零的 n×n方阵)的 n×n 方阵所生成的群;R 上的 n 级一般线性群 GL_n(R)定义为 R 上一切可逆的n×n 方阵所作成的群.在本文中我们证明了:若 R 是特征数≠2的可换整环(无零因     

6p阶2度有向Cayley图的正规性

群G的Cayley有向图X=Cay(G,S)叫做正规的,如果G的右正则表示R(G)在X的全自同构群Aut(X)中正规.决定了6p(p素数)阶2度有向Cayley图的正规性,发现了一个新的2度非正规Cayley有向图.     

U_3(F_9)和U_3(F_(25))的自同构

<正> 1952年,J.Dieudonne在总结典型群的研究成果时指出:若f是特征数≠2体K上的一个厄米特迹形式,在此假设下,有下述结论: 当n≥3时,除了群U_3(F_9)和U_3(F_(25))可能是例外,群U_n(K,f)的每一个自同构,都可以写作形状φ(u)=X(u)gug~(-1),其中g属于群ΓU_n(K,f)而X(u)是U_n(K,f)到它的中核之中的一个同态. 到现在为止仍未见到U_3(F_9)和U_3(F_(25))的叙述.本文从U_3(F_9)和U_3(F_(25))的结构     

广义超特殊p-群的自同构群Ⅲ

确定了广义超特殊P-群G的自同构群的结构.设|G|=p2n+m,|ζG|=pm,其中n≥1,m≥2,AutfG是AutG中平凡地作用在Frat G上的元素形成的正规子群,则(1)当G的幂指数是pm时,(i)如果p是奇素数,那么Aut G/AutfG≌Z(p_1)pm-2,并且AutfG/Inn G≌Sp(2n,p)×zp.(ii)如果p=2,那么AutG=AutfG(若m=2)或者AutG/AutfG≌Z2m-3×z2(若m≥3),并且AutfG/InnG≌Sp(2n,2)× z2.(2)当G的幂指数是pm+1时,(i)如果p是奇素数,那么AutG=<θ>×AutfG,其中p的阶是(p-1)pm-1,且AutfG/InnG≌K(×)Sp(2n-2,p),其中K是p2n-1阶超特殊p-群.(ii)如果p=2,那么Aut G=<θ1,θ2>(×) AutfG,其中<θ1,θ2>=<θ1>×<θ2>≌Z2m-2×Z2,并且AutfG/InnG≌K(×)Sp(2n-2,2),其中K是22n-1阶初等Abel 2-群.特别地,当n=1时,AutfG/InnG≌Zp.     

一类p-群的自同构群的阶

设 P 为奇素数,P~4阶群 G(121)=,a~p=b~p=c~p=d~p=1,[b,d]=a,[c,d]=b.本文给出了 G/Z(G)≌G_(121),Z(G)循环的群 G 的完全分类,并给出其中一些群的自同构群的阶,它们是自同构群的阶为 p~n 的p~(n-1)阶群,n≥6.从而完整地得到了:对一切奇素数 p,存在群 G 使|A(G)|=p~n 的最小 n 是6.     

广义超特殊p-群的自同构群(Ⅱ)

重新确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|ζG|=p~m,其中n≥1,m≥2,Aut_cG是AutG中平凡地作用在ζG上的元素形成的正规子群,则(i)若p是奇素数,则AutG=〈θ〉×Aut_cG,其中θ的阶是(p-1)p~(m-1);若p=2,则AutG=〈θ_1,θ_2〉×Aut_cG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2m-2)×Z_2.(ii)如果G的幂指数是p~m,那么Aut_cG/InnG≌Sp(2n,p).(iii)如果G的幂指数是p~(m+1),那么Aut_cG/InnG≌K×Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群(若p是奇素数)或者初等Abel 2-群.特别地,当n=1时,Aut_cG/InnG≌Z_p.     

广义超特殊p-群的自同构群Ⅲ

确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|■G|=p~m,其中n≥1,m≥2,Aut_fG是AutG中平凡地作用在Frat G上的元素形成的正规子群,则(1)当G的幂指数是p~m时,(i)如果p是奇素数,那么AutG/AutfG≌Z_((p-1)p~(m-2)),并且AutfG/InnG≌Sp(2n,p)×Zp.(ii)如果p=2,那么AutG=Aut_fG(若m=2)或者AutG/AutfG≌Z_(2~(m-3))×Z_2(若m≥3),并且AutfG/InnG≌Sp(2n,2)×Z_2.(2)当G的幂指数是p~(m+1)时,(i)如果p是奇素数,那么AutG=〈θ〉■Aut_fG,其中θ的阶是(p-1)p~(m-1),且Aut_f G/Inn G≌K■Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群.(ii)如果p=2,那么AutG=〈θ_1,θ_2〉■Aut_fG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2~(m-2))×Z_2,并且Aut_fG/Inn G≌K×Sp(2n-2,2),其中K是2~(2n-1)阶初等Abel 2-群.特别地,当n=1时...     

环的广义斜导子

设R是一个半素环, RF(resp．Q)是它的左Martindale商环(对称Martindale 商环),K是R的一个本质理想,则K上的每一个广义斜导子μ能被唯一地扩展到RF和Q 上．设R是一个素环,K是R的一个本质理想,μ是K上的一个广义斜导子且α为其伴随自同构,d为其伴随斜导子,如果存在n≥0,使得对任意的x∈K都有μ(x)n=0,那么μ=0．     

一类环上G_n(R)的自同构

设R是连通可和环, 2是R的单位。R上一切形如■的可逆上三角阵构成的乘法群为G_n(R),设Λ是G_n(R)的自同构,则Λ必为以下形状之一; 其中P∈G_n(R),σ是R的自同构; 其中τ是R的自同构,p(A)是A的(n,n)位置的元素。     

2×2 上三角算子矩阵的 Drazin 谱

设M_C= [ AC ; 0 B ]是从Hilbert空间H K 到HK 中的 2×2 上三角算子矩阵. 该文主要研究 M_C的Drazin可逆性和M_C 的 Drazin谱.此外, 对给定算子A∈B}(H) 和 B∈B}(K), 将给出在一定条件下所有上三角算子矩阵M_C的Drazin谱的交∩σ_D (M_C) 的具体表达式.     

On short wave stability and sufficient conditions for stability in the extended Rayleigh problem of hydrodynamic stability

We consider the extended Rayleigh problem of hydrodynamic stability dealing with the stability of inviscid homogeneous shear flows in sea straits of arbitrary cross section. We prove a short wave stability result, namely, if k > 0 is the wave number of a normal mode then k > k _c (for some critical wave number k _c) implies the stability of the mode for a class of basic flows. Furthermore, if $ K(z) = \frac{{ - (U'_0 - T_0 U'_0 )}} {{U_0 - U_{0s} }} $ K(z) = \frac{{ - (U'_0 - T_0 U'_0 )}} {{U_0 - U_{0s} }} , where U ₀ is the basic velocity, T ₀ (a constant) the topography and prime denotes differentiation with respect to vertical coordinate z then we prove that a sufficient condition for the stability of basic flow is $ 0 < K(z) \leqslant \left( {\frac{{\pi ^2 }} {{D^2 }} + \frac{{T_0^2 }} {4}} \right) $ 0 < K(z) \leqslant \left( {\frac{{\pi ^2 }} {{D^2 }} + \frac{{T_0^2 }} {4}} \right) , where the flow domain is 0 ≤ z ≤ D.     

特征不为 2 的有限域上酉群的极小生成元集

设K=Fq2为含有q2个元素的有限域,q为奇素数的幂,*：a→a*=aq是Fq2的一个二阶自同构．本文用几何方法证明了除K为F32而n=4的情形外,Fq2上的酉群Un（V）可由2个元素生成．     

The correlations of finite Desarguesian planes, Part I: Generalities

The polarities of Desarguesian planes have long been known. This author has undertaken to classify the correlations of finite Desarguesian planes in general. In [6] we have presented all the correlations with identity companion automorphism which are not polarities, of these planes. In this sequence of papers, we classify the correlations of planes of order $ p^{2^{i}(2n+1)}, n \neq 0 $, with companion automorphism ( $p^{2^{i}t}$ ), p an odd prime, $ t \neq 0 $. This represents a complete classification of the correlations of planes of odd nonsquare order (i = 0). Some of the correlations of planes of odd square order ($ t \neq 0 $ ) are also covered by the present analysis.When the companion automorphism is not trivial, the problem, naturally, becomes more involved, and a great deal begins to hinge upon the order of the plane being odd or even, and also a square or a nonsquare.The correlations of planes of order $ 2^{2^{i}(2n+1)}, n \neq 0 $, with companion automorphism $ 2^{2^{i}t}, t \neq 0 $, and especially those of planes of order $ p^{2^{i}(2n+1)}, i \neq 0 $, with companion automorphism $ p^{2^{j}(2r+1)}, j > i $ require a substantially different treatment, and will be the object of separate efforts.     

On a theorem of J. Vukman

Summary LetR be a ring. A bi-additive symmetric mappingD:R × R R is called a symmetric bi-derivation if, for any fixedy R, the mappingx D(x, y) is a derivation. J. Vukman [2, Theorem 2] proved that, ifR is a non-commutative prime ring of characteristic not two and three, and ifD:R × R R is a symmetric bi-derivation such that [D(x, x), x] lies in the center ofR for allx R, thenD = 0. This result is in the spirit of the well-known theorem of Posner [1, Theorem 2], which states that the existence of a nonzero derivationd on a prime ringR, such that [d(x), x] lies in the center ofR for allx R, forcesR to be commutative. In this paper we generalize the result of J. Vukman mentioned above to nonzero two-sided ideals of prime rings of characteristic not two and we prove the following. Theorem.Let R be a non-commutative prime ring of characteristic different from two, and I a nonzero two-sided ideal of R. Let D: R × R R be a symmetric bi-derivation. If [D(x, x), x] lies in the center of R for all x I, then D = 0.     

从属解析函数族的有限阶哈达玛乘积

设P[A,B]={f(z):f(z)(?)(1+Az)/(1-Bz),A+B≠0,|B|≤1,f(z)在单位开圆盘内解析}.定义函数族H_1,H_2,…,H_n的有限阶哈达玛乘积为H_1*H_2*H_3…*H_n(z)={f_1*f_2*f_3*…f_n(z):f_i∈H_i,i=1,2,…,n,n∈Z~+}.讨论并得到了P(A_1,B_1)*P(A_2,B_2)*P(A_3,B_3)*…*P(A_n,B_n)=P(X,Y)的充分必要条件,主要结果是对先前相应研究内容的直接推广.     

Fixed points of involutive automorphisms of the Bruhat order

Applying a classical theorem of Smith, we show that the poset property of being Gorenstein^* over Z₂ is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. Incitti. We also show that the Bruhat order on the fixed points of an involutive automorphism induced by a Coxeter graph automorphism is isomorphic to the Bruhat order on the fixed subgroup viewed as a Coxeter group in its own right.     

Uniqueness theorem for measures in C(K) and its application in the theory of random processes

Let (, , P) be a probability space, let K be a separable Hausdorff topological space, and let :×K be a random process with continuous realizations on K. By the deviation of the random process from the function aC(K) we mean the random variable . It is proved in the paper that the random process is uniquely determined by the p-th moments of its deviations from continuous functions for a fixed p, p0, 2, 4, 6, .... The basis of the proof is the uniqueness theorem for measures in C(K), generalizing the uniqueness theorem for measures of order p on the line and refining the Hoffman-Jørgensen result on measures that coincide on the balls of the space C(K).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 119, pp. 144–153, 1982.