‎a ring $r$ is strongly clean provided that every element‎ ‎in $r$ is the sum of an idempotent and a unit that commutate‎. ‎let‎ ‎$t_n(r,sigma)$ be the skew triangular matrix ring over a local‎ ‎ring $r$ where $sigma$ is an endomorphism of $r$‎. ‎we show that‎ ‎$t_2(r,sigma)$ is strongly clean if and only if for any $ain‎ ‎1+j(r)‎, ‎bin j(r)$‎, ‎$l_a-r_{sigma(b)}‎: ‎rto r$ is surjective‎. ‎furt...

‎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.

The electronic conductance at zero temperature through a quantum wire with side-connected asymmetric quantum ring (as a scatter system) is theoretically studied using the non-interacting Hamiltonian Anderson tunneling method. In this paper we concentrate on the configuration of the quantum dot rings. We show that the asymmetric structure of QD-scatter system strongly influences the amplitude an...

‎We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel‎, ‎that is‎, ‎every simple right $R$-module has a flat $B$-cover‎. ‎We give some properties of such rings along with examples‎. ‎We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...

the concepts of fuzzy semi-ideals of r with respect to h≤r and generalized fuzzy quotient rings are introduced. some properties of fuzzy semiideals are discussed. finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

abstract background and objective: vascular abnormality and dysfunction plays an important role in the pathogenesis of vascular disease in diabetic state. in this study, we aimed to investigate whether an in vitro exposure of endothelium-intact aortic rings to melissa officinalis (lemon balm, mo) aqueous extract could have a beneficial effect in rats with subchronic diabetes. materials and meth...

‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...