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...

‎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 A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be Bézout is also studied, but a response is only given in the case where pSpec(A) (a quotient space of Spec(A)) is totally disconnected. Trivial ring extensions which are fqp-rings are cha...

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...