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.

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.

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

cycloaddition reaction between c30 and hula-i, 3-diene was studied within the snimework of am i (rhf)level. the reaction involving the double bond between two hexagons and a hexagon and a pentagon, as wellas the cycloaddition products followed by disrotatory ogs s electrocyclic ring openings were considered.thermodynamics parameters and stability energy and innsation state are evaluated in thre...

In the title compound, C(34)H(28)N(2)O(2)S, the piperidine ring adopts a chair conformation. One of the pyrrolidine rings adopts an envelope conformation with the methyl-ene C atom at the flap whereas the other pyrrolidine ring and the thia-zolidine ring adopt half-chair conformations. The mean plane of the dihydro-acenaphthyl-ene ring system [maximum deviation = 0.067 (1) Å] makes dihedral ang...

Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the...

In the mol-ecule of the title compound, C(18)H(13)Cl(2)N(3)O(2)S(2), the thia-zolidinone ring has an envelope conformation with the S atom displaced by 0.394 (3) Å from the plane of the other ring atoms. The thia-diazole ring is oriented at a dihedral angle of 7.40 (4)° with respect to the 4-methoxy-phenyl ring. Intra-molecular C-H⋯S, C-H⋯N and C-H⋯Cl hydrogen bonds result in the formation of t...