广义导子幂中心化子条件

设R是半素环,U是R的极大右商环,C是R的扩展型心,a,b∈U．对R上广义导子δ的值的幂零,幂中心化子问题进行了讨论,即(aδ(x))~nb=0(∈C)形式的恒等式,对δ的形式以及δ与a,b的关系做了完整的刻画,从而发展了Herstein,Brear的研究结果．     

广义导子幂中心化子条件(英文)

设R是素环,U是R的极大右商环,C是R的扩展型心,I是R的非零理想,δ是R上的广义导子,a,b,q∈U.本文给出了恒等式(aδ(qx)-bx)~n=0(∈C在I上成立的充分必要条件,得到的结果推广了Herstein,Lanski,Lee的结论.     

双重导子的连续性

双重导子是导子的一种推广形式.令δ和ε为复线性代数A到自身内的两个映射,称A到自身内的线性映射d是一个(δ,ε)-双重导子,如果对任意a,b∈A,有d(ab)=d(a)b+ad(b)+δ(a)ε(b)+ε(a)δ(b)成立.本文研究Banach代数上双重导子的自动连续性问题,证明如果δ和ε为含单位元C~*-代数上的两个在0点连续的映射,则该C~*-代数上的每个(δ,ε)-双重导子都是自动连续的.     

幂零群的一个反例

设R是含1环,I是R的幂零子环(即存在自然数n,使得In=0),作为R的子环,设I是由xj(j∈J)生成的.记U=1+I,它是幂零类n-1的幂零群,把U的由1+xj(j∈J)生成的子群记为G.本文构造的群例表明:G的幂零类能够小于U的幂零类.     

带有广义导子的素环

The concept of derivations and generalized inner derivations has been generalized as an additive function δ: R→ R satisfying δ(xy) = δ(x)y xd(y) for all x,y∈R,where d is a derivation on R.Such a function δis called a generalized derivation.Suppose that U is a Lie ideal of R such that u2 ∈ U for all u ∈U.In this paper,we prove that U(C)Z(R) when one of the following holds:(1)δ([u,v]) = uov (2)δ([u,v]) uov=O(3)δ(uov) =[u,v](4)δ(uov) [u,v]= O for all u,v ∈U.     

套代数上的κ-Jordan可导映射

令β是维数大于1的Hilbert空间H上的套,algβ为相应的套代数.k为一非零有理数.本文证明了algβ上的k-Jordan可导映射,即δ(k(ab+ba))=k(δ(a)b+aδ(b)+δ(b)a+bδ(a)),(?)a,b∈algβ,是algβ上的可加导子.特别地,当H是无限维时,δ是内导子.我们也给出了k-Jordan三重可导映射的相应结果.     

算子代数上(m,n)-Jordan导子的刻画

设R是一个环,M是一个R-双边模,m和n是两个非负整数满足m+n≠0,如果δ是一个从R到M的可加映射满足对任意A∈R,(m+n)δ(A~2)=2mAδ(A)+2nδ(A)A,则称δ是一个(m,n)-Jordan导子.本文证明了,如果R是一个单位环,M是一个单位R-双边模含有一个由R中幂等元代数生成的左(右)分离集,那么,当m,n0且m≠n时,每一个从R到M的(m,n)-Jordan导子恒等于零.还证明了,如果A和B是两个单位环,M是一个忠实的单位(A,B)-双边模(N是一个忠实的单位(B,A)-双边模),m,n0且m≠n,U=[A N M B]是一个|mn(m-n)(m+n)|-无挠的广义矩阵环,那么每一个从U到自身的(m,n)-Jordan导子恒等于零.     

素环上的T—导子

设R是一环,可加映射d称为T－导子,如果对于任意a,b∈R,有d(ab)=T(a)d(b) d(a)T(b),其中T是R的非恒等自同态,本引入素环上T－导子的概念,研究其性质,并得出两个主要结果。     

关于素环广义导子和对称双导的几点备注

设R是素环,I是R的非零理想,如果R容许一个非单位映射的左乘子使得对所有x,y∈I满足δ(x°y)=x°y或δ(x°y) x°y=0,那么R可交换.此外,如果R是2-扭自由的素环,U是平方封闭的李理想,γ是伴随导子非零的广义导子,B:R×R→R是迹函数为g(x)=B(x,x)的对称双导,当下列条件之一成立时U为中心李理想(1)γ同态作用于U(2)2[x,y]-g(xy) g(yx)∈Z(R)(3)2[x,y] g(xy)-g(yx)∈Z(R)(4)2(x°y)=g(x)-g(y)(5)2(x°y)=g(y)-g(x)对所有的x,y∈U.     

具有稳定秩1的置换环

称环R具有稳定秩1,如果对任意的a,b∈R,aR bR=R,则存在Y∈R,使得a by∈U(R).证明了置换环有稳定秩1当且仅当对任意的幂等元e∈R,如果aR b(eR)=R,则存在u,v∈R,使得au b(ev):0且(eR)u (eR)(ev)=eR当且仅当对任意的幂等元e∈R,如果aR b(eR):R,则存在u,t,∈R,使得as b(et)=0当且仅当存在z∈eR,使s=uz,t=vz,从而给出这类置换环新的元素刻画.进一步地,证明了如果R是稳定秩1的置换环,对任意的正则元a∈R,2a总可以表示成两个单位的和.最后对具有降链本原分式的置换环R,证明了对任意的a∈R,2a总可以表示成两个单位的和.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Isomorphisms of Lattices of Subalgebras of Semifields of Positive Continuous Functions

Siberian Mathematical Journal - We consider the lattice of subalgebras of a semifield U(X) of positive continuous functions on an arbitrary topological space X and its sublattice of subalgebras...     

Regularity of minimizers of non-isotropic integrals of the calculus of variations

The regularity of the minimizers of a special type of non-isotropic variational minimization problem is studied. The particularity of the potential of energy is that it has different growth rate with respect to different parts of the derivatives of the function. In particular, the model treated in this paper can be described as $$\Phi (Du) = |\partial _1 u|^2 + |\partial _2 u|^2 + |\partial _3 u|^2 + |\partial _3 u - |^p .$$ By using a result of P.Marcellini (cf. [4]) and perturbation method, it is proved that the minimizer of the Dirichlet boundary value problem is a function of W _loc ^{1, ∞} .