we introduce center-like subsets z*(r,f), z**(r,f) and z1(r,f), where r is a ring and f is a map from r to r. for f a derivation or a non-identity epimorphism and r a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of r.

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

Background Vascular ring is less than 1% of congenital heart disease. Double aortic arch (DAA) is the most common form of it.  Its detecting is important because of the effects of pressure on the esophagus and trachea. Case Report In this study, three children suffering from double aortic arch with symptoms of dysphagia and recurrent aspiration, which in two cases had led to cardiac arrest, wer...

elongation. The recycling of ITA grafts can be performed in only a selected redo CABG population, when the ITA is patent but stenotic in the perianastomotic area, when there is a stenosis in the coronary artery distal to the anastomosis, and when an interventional cardiologic approach is not feasible. Preoperative selective angiography of the used ITA is helpful to exclude proximal stenosis, to...

A 61-year-old woman presented with the primary complaints of chest heaviness and dysphagia over the past 10 years. Extensive work-up included a computerized tomographic angiography that revealed a right aortic arch with an aberrant left subclavian artery with a vascular ring completed by the fibrotic ligamentum arteriosum connecting the proximal aberrant left subclavian artery to the left pulmo...

Figura 1 Angio-TC torácica con reconstrucción VR-3D, visión posterosuperior. En esta imagen podemos observar un arco aórtico completo, con origen independiente de los troncos supraaórticos: en el arco izquierdo, ligeramente de mayor calibre, se originan la arteria carótida y subclavia izquierdas y en el arco derecho, la arteria carótida, vertebral y subclavia derechas. AAo: ascending aorta (aor...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . doi:10.1093/ehjci/jet252 Online publish-ahead-of-pr...

To cite: Sharma A, Malhi AS, Kumar S, et al. BMJ Case Rep Published online: [please include Day Month Year] doi:10.1136/ bcr-2016-216265 DESCRIPTION A 3-month-old girl child presented with a history of respiratory distress, rapid breathing and mild cyanosis since birth. Auscultation revealed systolic murmur (3/6) in the right parasternal and upper left parasternal area. ECG showed right axis de...

a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.