We give some new properties of almost injective modules and their endomorphism rings, and also provide conditions as to when a direct sum of almost injective (or CS) modules is again almost injective (or CS) in some special cases..

The title compound, C(15)H(13)ClN(6), contains two pyrimidine rings and one benzene ring, where the dihedral angle between the planes through the pyrimidine rings is 81.57 (10)°, and those between the pyrimidine rings and the benzene ring are 84.02 (8) and 89.46 (7)°, indicating that the three rings are almost perpendicular. In the crystal, inter-molecular N-H⋯N hydrogen bonds link the mol-ecul...

Since the discovery and implication of N-ethylmaleimide-sensitive factor (NSF)-attachment protein receptor (SNARE) proteins in membrane fusion almost two decades ago, there have been significant efforts to understand their involvement at the molecular level. In the current study, we report for the first time the molecular interaction between full-length recombinant t-SNAREs and v-SNARE present ...

‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...

Let $R$ be a commutative ring. An $R$-module $M$ is called semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ $\GV$-torsion for any finitely generated ideal $I$. In this article, we show that the class of modules covering class. Moreover, introduce dimensions $R$-modules and $sr$-$w$-weak global ring $R$. Utilizing these notions, give some homological characterizations $\WQ$-rings $Q_0$-\PvMR s.

The title compound, C(60)H(88)O(4)·4CHCl(3)·2H(2)O, is the alkyl-ated product of 5,11,17,23-tetra-tert-butyl-calix[4]arene. It adopts a distorted cone conformation which leads to an open cavity. All the phenolic rings are tilted so that their tert-butyl groups are pitched away from the calix cavity. Two opposite aromatic rings are close to being perpendicular to one another [dihedral angle 85.0...

A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.

We construct stationary solutions possessing two vortex rings to the nonlinear Schrödinger type problem iut = −ε4u + ( V + |u| ) u, where the unknown function u is defined as u : R3×R→ C, ε is a small positive parameter and V is a real smooth potential. These two vortex rings will be pinned at a fixed site by the potential V . They lie in the same plane and have neighboring interaction in the n...

We first explain the historical and logical relations of hyperstructures introduced by M. Krasner and R. Rota, and generalized by T. Vougiouklis. Then, with our new algorithm based on our previous results on hypergroups and H v-groups of order 2, 3 and 4, we enumerate hyperrings and H v-rings. More precisely, we found 63 hyperrings of order 2, 875 H v-rings of order 2 and 33,277,642 hyperrings ...