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.

Reduction of ovarian steroids at menopause leads to significant changes in the urogenital tract. These changes often worsen with time, particularly in nonsmokers, affecting up to 38% of menopausal women. Urogenital symptoms that clearly respond to estrogen therapy include atrophic vaginitis, dryness, and accompanying dyspareunia. Estrogen reduces urinary tract infections in women plagued by fre...

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.

premature rupture of membrane (prom) is one of the complications of pregnancy which is blamed for increasing the rate of cesarean. therefore, we studied pregnant women who were admitted in shariati hospital during march 1996 and march 2000, to determine the rate of cesarean delivery in cases with prom after 36th week of pregnancy (term prom). in a retrospective study, we included pregnant women...