The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...

we give a survey of recent applications of group rings to combinatorics and tocryptography, including their use in the di erential cryptanalysis of block ciphers.

The transport of Balbiani ring (BR) premessenger RNP particles in the larval salivary gland cells of the dipteran Chironomus tentans can be followed using electron microscopy. A BR RNP particle consists of an RNP ribbon bent into a ringlike structure. Upon translocation through the nuclear pore complex (NPC), the ribbon is straightened and enters the central channel of the NPC with the 5' end o...

An efficient N-heterocyclic carbene (NHC) catalyzed sulfenylation reaction of α,β-unsaturated aldehydes with N-(arylthio)phthalimide has been developed. A wide variety of α-thioenals can be obtained with good to excellent yields and excellent Z-configuration.

In this paper we construct a q-deformation of the Witt-Burnside ring of a profinite group over a commutative ring, where q ranges over the ring of integers. When q = 1, this coincides with the Witt-Burnside ring introduced by A. To achieve our goal we show that there exists a q-deformation of the necklace ring of a profinite group over a commutative ring. As in the classical case, i.e., the cas...

The following result is proved: Let R be a 2-torsion free semiprime ring, and let T : R → R be an additive mapping, related to a surjective homomorphism θ : R → R, such that 2T (x2) = T (x)θ(x) + θ(x)T (x) for all x ∈ R. Then T is both a left and a right θ-centralizer.

Let R be a commutative ring and Z(R) the set of all zero divisors R. Γ(R) is said to divisor graph if x,y ∈ V (Γ(R)) = (x,y) E(Γ(R)) only x.y 0. In this paper, we determine total vertex irregularity strength graphs associated with rings ℤp2 × Zq for p,q prime numbers.

Recall that a regular local ring is a noetherian local ring with dimension equal to dimkm/m. A regular local ring of dimension one is precisely a discrete valuation ring. If V is a nosingular variety then t(V ) is a scheme with all local rings regular, so t(V ) is clearly regular in codimension one. In this section we will consider schemes satisfying the following condition: (∗) X is a noetheri...

In the crystal structure of the title compound, [V(2)(C(22)H(21)N(2)O(2))(2)O(4)]·2H(2)O, oxide-bridged dimers of the complex are linked to water mol-ecules by hydrogen-bonding inter-actions. The two five-membered chelate rings in the dimeric mol-ecule both adopt twist conformations. Each V(V) atom is six-coordinated by one oxide group and by two N and one O atom of the tridentate Schiff base l...