in this article‎, ‎we have characterized ideals in $c(x)$ in which‎ ‎every ideal is also an ideal (a $z$-ideal) of $c(x)$‎. ‎motivated by‎ ‎this characterization‎, ‎we observe that $c_infty(x)$ is a regular‎ ‎ring if and only if every open locally compact $sigma$-compact‎ ‎subset of $x$ is finite‎. ‎concerning prime ideals‎, ‎it is shown that‎ ‎the sum of every two prime (semiprime) ideals of e...

In the title compound, C(14)H(13)NOS, the dihedral angle formed by the mean planes through the indane ring system and the thio-phene ring is 85.04 (11)°. The imine bond is located in the thio-phene plane [the S-C-C-N torsion angle is 0.00 (3)°] and an intra-molecular O-H⋯N hydrogen bond is observed.

In the title compound, C(12)H(11)FN(4)O(2), the pyridine ring is connected to a benzene ring by a -CH(2)-NH(2)- chain. The nitro group is twisted out of the pyridine ring plane [torsion angle O-N-C-C = 10.41 (10)°]. An intramolecular N-H⋯O hydrogen bond occurs. The fluoro-benzene ring is disordered over two positions [occupancy ratio = 0.59 (3):0.41 (3)]. Inter-molecular N-H⋯O and N-H⋯N hydroge...

The electronic absorption and emission spectra of the [n]cycloparaphenylenes with n = 6,7,...,11 ([n]CP) have been studied at the time-dependent density functional theory level. The calculations show that the optical gap increases with increasing size of the ring due to reduced ring strain in the larger carbon nanohoops, whereas the energy of the first bright state follows the opposite trend fo...

In the present note, we discuss certain observations made by the author in February 2009 concerning strongly torsion-free profinite groups [cf. [Mzk2], Definition 1.1, (iii)]. These observations grew out of e-mail correspondences between the author, Akio Tamagawa, and Marco Boggi, as well as oral discussions between the author and Akio Tamagawa. Definition 1. Let G be a profinite group. (i) We ...

in this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right rees factor, cyclic and acts in general  implies some other properties, respectively.

N. Metropolis and G.-C. Rota Adv. Math, 50, 1983, 95{125] studied the necklace polynomials, and were lead to deene the necklace algebra as a combinatorial model for the classical ring of Witt vectors (which corresponds to the multiplicative formal group law X + Y ? XY). In this paper, we deene and study a generalized necklace algebra, which is associated with an arbitrary formal group law F ove...

In the title compound, C(16)H(17)ClN(4)O(2), the aromatic ring is twisted slightly with respect to the plane of the diazene group [N-N-C-C torsion angle = -3.9 (4)°]. The NO(2) group is twisted by 16.2 (4)° relative to the aromatic ring. The two ethyl chains are positioned such that one ethyl chain lies above and the other below the ring.