上三角矩阵的线性交换映射的表示

设Trn(R)表示定义在实数域R上的n×n阶上三角矩阵的集合,φ是定义Trn(R)上线性映射.如果对任意X∈Trn(R)有Xφ(X)=φ(X)X成立,称φ是线性交换映射.本文利用初等的矩阵计算方法描述了当φ(I)=I时,线性交换映射φ的表示形式,而且给出了φ的Frobenius范数‖φ(X)‖F的估计.     

m-Power Commuting MAPS on Semiprime Rings

Let R be a semiprime ring with center Z(R), extended centroid C, U the maximal right ring of quotients of R, and m a positive integer. Let f: R → U be an additive m-power commuting map. Suppose that f is Z(R)-linear. It is proved that there exists an idempotent e ∈ C such that ef(x) = λx + μ(x) for all x ∈ R, where λ ∈C and μ: R → C. Moreover, (1 ? e)U ? M₂(E), where E is a complete Boolean ring. As consequences of the theorem, it is proved that every additive, 2-power commuting map or centralizing map from R to U is commuting.     

Decompositions of Quotient Rings and m-Power Commuting Maps

Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = X ⁿ h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q ₁ ⊕ Q ₂ ⊕ Q ₃ such that Q ₁ is a ring satisfying S _2n?2, the standard identity of degree 2n ? 2, Q ₂ ? M _n (E) for some commutative regular self-injective ring E such that, for some fixed q > 1, x ^q  = x for all x ∈ E, and Q ₃ is a both faithful S _2n?2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring.     

On centralizers of standard operator algebras and semisimple H*-algebras

Summary Let Abe a semisimple H*-algebra and let T: A→Abe an additive mapping such that T(x ^{n +1})<span lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>=T(x)x ⁿ+x ⁿ T(x) holds for all x∈Aand some integer n≥1. In this case Tis a left and a right centralizer.     

Orthogonality of Generalized (θ,φ)-Derivations on Ideals

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized (θ,φ)-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

中心多项式与环的交换性

本文证明了环的一个交换性定理,它是文献[6-8]中相应结论的推广,     

Biderivations,linear commuting maps and commutative post-Lie algebra structures on W-algebras

In this paper, the biderivations without the skew-symmetric condition of W-algebras including the Witt algebra, the algebra W(2,2) and their central extensions are characterized. Some classes of non-inner biderivations are presented. As applications, the forms of linear commuting maps and the commutative post-Lie algebra structures on aforementioned W-algebras are given.     

半素环上(右)广义自同构的扩张

In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.     

Polynomial and Regular Maps into Grassmannians

We find a regular deformation retraction _n,r (K): Idem _n,r (K) G _n,r (K) from the manifold Idem _n,r (K) of idempotent n × n matrices with rank r to the Grassmannian manifold G _n,r (K) over K the reals, complex numbers or quaternions. Then we derive an injection from the sets of homotopy classes of complex-valued polynomial to such a set of real-valued regular maps, where denotes the Zariski closure in the affine space ⁿ of a subset ⁿ . Furthermore, we list complex-valued polynomial maps ^{2 2} of any Brouwer degree and deduce that the map ()_2,1: Idem()_2,1 G()_2,1 yields an isomorphism [ ² ] [ ², ²] of cyclic infinite homotopy groups. Finally, we show that every nonzero even Brouwer degree of the spheres ⁿ and ⁿ cannot be realized by a real-valued (resp. complex-valued) homogeneous polynomial map provided that n is even.     

Biderivations of the planar Galilean conformal algebra and their applications

In this paper, the biderivations without skew-symmetric condition of the planar Galilean conformal algebra are presented. As applications, the characterizations of the forms of linear commuting maps and the commutative post-Lie algebra structures on the planar Galilean conformal algebra are given.     

环上带有广义导子和自同构的恒等式

设R是一个素环,RF是它的左Martindale商环.如果φ(xigik△ij)是环R的某个本质理想I的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(zikj)是环RF的一个广义多项式恒等式.设R是一个具有特征P≥0的半素环,RF是它的左Martindale商环.如果φ(xigik△ijfik)是环R的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(zikjfike(△ij)是环RF的一个广义多项式恒等式,这里fik和e(△ij)是RF中的幂等元.