‎let $r$ be a ring with involution $*$‎. ‎an additive mapping $t:rto r$ is called a left(respectively right) centralizer if $t(xy)=t(x)y$ (respectively $t(xy)=xt(y)$) for all $x,yin r$‎. ‎the purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

h6-benzne, h6-garphyne) was studied with MPW1PW91 quantum chemical computations. Quantumtheory of atoms in molecules (QTAIM) was applied to elucidate these complexes Cr-CO bonds. Theellipticity (e) and h values of the Cr-CO bonds were calculated. The amount of pp-dp back-donation ofCr-CO bonds were illustrated by calculation of the magnitude of the quadrupole polarization of c...

Let $R$ be a ring, $n$ an non-negative integer and $d$ positive or $\infty$. A right $R$-module $M$ is called \emph{$(n,d)^*$-projective} if ${\rm Ext}^1_R(M, C)=0$ for every $n$-copresented $C$ of injective dimension $\leq d$; ring \emph{right $(n,d)$-cocoherent} with $id(C)\leq d$ $(n+1)$-copresented; $(n,d)$-cosemihereditary} whenever $0\rightarrow C\rightarrow E\rightarrow A\rightarrow 0$ e...

In this paper, some familiar and new results on arithmetical rings, modules, Bezout rings (not necessarily commutative) are provided. particular, we examine relationships between their localizations by maximal ideals, saturated submodules saturations, localizable properties of annihilators finitely generated modules over diagonalizable with flat right quasi-projective Hermite Pierce stalks, Kru...

A silver-free methodology was developed for the synthesis of unprecedented N-heterocyclic carbene ruthenium indenylidene complexes bearing a bidentate picolinate ligand. The highly stable (SIPr)(picolinate)RuCl(indenylidene) complex 4a (SIPr = 1,3-bis(2-6-diisopropylphenyl)imidazolidin-2-ylidene) demonstrated excellent latent behaviour in ring closing metathesis (RCM) reaction and could be acti...

We investigate the sufficient conditions and the necessary conditions on an exchange ring R under which R has stable range one. These give nontrivial generalizations of Theorem 3 of V. P. Camillo and H.-P. Yu (1995), Theorem 4.19 of K. R. Goodearl (1979, 1991), Theorem 2 of R. E. Hartwig (1982), and Theorem 9 of H.-P. Yu (1995). 2000 Mathematics Subject Classification. Primary 16E50, 19B10. An ...

-, “Generalized Riccati equations for two-point boundaly value descriptor systems,” in Proc. 26th IEEE Conf: Decision Contr., Los Angeles, CA, 1987. H. E. Rauch, F. Tung, and C. T. Striebel, “Maximum likelihood estimates of linear systems,” J. AZAA, vol. 3, pp. 1445-1450, 1965. L. R. Riddle and H. L. Weinert, “Fast algorithms for the reconstruction of images from hyperbolic systems,” in Proc. 2...

It is well-known that evaporation of sessile drops with suspended particles like colloids and coffee powders can yield a variety of two-dimensional patterns depending on the particle shapes and internal flow patterns. Here we show that ordered three-dimensional structures can be built via evaporation of saline drops on highly hydrophobic substrates like pristine PP (polypropylene) with micropor...

Introduction. L. Fuchs [2 ] has given for Noetherian rings a theory of the representation of an ideal as an intersection of primal ideals, the theory being in many ways analogous to the classical Noether theory. An ideal Q is primal if the elements not prime to Q form an ideal, necessarily prime, called the adjoint of Q. Primary ideals are necessarily primal, but not conversely. Analogous resul...