Let G = [ A M N B ] be a generalized matrix algebra defined by the Morita context (A,B,A MB,B NA,ΦMN ,ΨNM) . In this article we mainly study the question of whether there exist the so-called “proper” Jordan derivations for the generalized matrix algebra G . It is shown that if one of the bilinear pairings ΦMN and ΨNM is nondegenerate, then every antiderivation of G is zero. Furthermore, if the ...

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert C∗-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert C∗-module M over a C∗-algebra A as a oneparameter group of unitaries on M and prove that if α : R → U(M) is a dynamical system, where U(M) denotes the set of all unitary operator on M, th...

Let F be a commuting generalized derivation, with associated derivation d, on a semiprime ring R. We show that d(x)[y, z] = 0 for all x, y, z ∈ R and d is central. We define and characterize dependent elements of F and investigate a decomposition of R relative to F . Mathematics Subject Classification: 16N60, 16W25

Let gl(n, R) be the Lie algebra consisting of all n × n matrices over a commutative ring R with identity 1. In this paper, we prove that every generalized Lie triple derivation of gl(n, R)(n ≥ 2) is the sum of a Lie triple derivation and a homothety.

Let R be a ring with involution ′∗′. A map δ of the ring R into itself is called a derivation if δ(xy) = δ(x)y + xδ(y) for all x, y ∈ R. An additive map F : R → R is called a generalized derivation on R if F(xy) = F(x)y + xδ(y) for all x, y ∈ R, Permanent address: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh202002, India 292 Shakir Ali and Husain Alhazmi whe...

The k-center problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality, so that the maximum distance of any node to its nearest center is minimized. In this paper, we consider a generalization of this problem where, given a number p, we wish to place k centers so as to minimize the maximum distance of...

In this study, we define the generalized symmetric bi-derivation and its trace on MV-algebras give examples. We investigate some properties of bi-derivation’s trace. introduce isotone bi-additive bi-derivation. show that if A is a linearly ordered MV-algebra, Γ related to D γ , then = 0 or γ1 1

Beta-splines are a class of splines with applications in the construction of curves and surfaces for computer-aided geometric design. One of the salient features of the Beta-spline is that the curves and surfaces thus constructed are geometrically continuous, a more general notion of continuity than the one used in ordinary B-splines. The basic building block for Beta-splines of order k is a se...