Let $R$ be a ring and $M$ a right $R$-module. We call $M$, coretractable relative to $overline{Z}(M)$ (for short, $overline{Z}(M)$-coretractable) provided that, for every proper submodule $N$ of $M$ containing $overline{Z}(M)$, there is a nonzero homomorphism $f:dfrac{M}{N}rightarrow M$. We investigate some conditions under which the two concepts coretractable and $overline{Z}(M)$-coretractable...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

purpose: to describe a new noninvasive method to assure correct orientation of donor lenticules in descemet stripping automated endothelial keratoplasty (dsaek) surgery. methods: dsaek surgery was performed in three eyes with the diagnosis of pseudophakic bullous keratopathy (pbk). for the laboratory part of the study, two whole globes and two precut corneoscleral buttons were used. the donor l...

in this paper, a new design of optical channel drop filter based on two- dimensional photonic crystal ring resonators with triangular lattice is proposed. the rods of this structure is silicon with the refractive index nsi=3.46 and the surrounding environment is air with the refractive index of nair=1.the widest photonic band gap obtains for the filling ratio of r/a = 0.2. the filter’s transmis...

let a; b; k 2 k and u ; v 2 u(k). we show for any idempotent e 2 k, ( a 0 b 0 ) is e-clean i ( a 0 u(vb + ka) 0 ) is e-clean and if ( a 0 b 0 ) is 0-clean, ( ua 0 u(vb + ka) 0 ) is too.

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

in this work, new biodegradable abcba type pentablock copolymers with different mole ratio of l-lactide and ppdo-b-peg-b-ppdo triblock copolymer were synthesized and characterized. in the first step, ppdo-b-peg-b-ppdo triblock copolymer was synthesized via a ring-opening polymerization of p-dioxanone (pdo) monomer with poly (ethylene glycol) (peg) using stannous octoate (sn(oct)2) as the cataly...

results the mean udva (logmar) improved significantly from 1.13 ± 0.21 preoperatively to 0.24 ± 0.13 postoperatively (p < 0.001), and the mean cdva (logmar) improved significantly from 0.39 ± 0.12 to 0.19 ± 0.09 (p < 0.001). the mean cylinder of manifest refraction decreased significantly by 4.00 diopter (d) (p < 0.001). the mean spherical equivalent error (se) decreased significantly from −6.0...

purpose: to assess the stability of visual and refractive outcomes that was compared between three and 12 months after myoring implantation in moderate and severe keratoconus methods: this study included 54 eyes of 50 patients (27 males and 23 females) with stage ii and iii keratoconus who underwent myoring (dioptex gmbh) implantation. clinical outcomes including uncorrected distance visual acu...

let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...