In this paper, we introduce the new notion of strongly J-clean rings associated with polynomial identity g(x) = 0, as a generalization of strongly J-clean rings. We denote strongly J-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-J-clean rings. Next, we investigate some properties of strongly g(x)-J-clean.

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 ...

in this paper we study some results on noetherian semigroups. we  show that if  $s_s$ is an  strongly  faithful $s$-act and $s$ is a duo weakly noetherian, then we have the following.

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.

Artificial Intelligence (AI) is a term frequently encountered in every day life, thus proving its significant applicability on a wide range of fields. Among these fields, some of the more popular ones include playing games competitively and decision theory problems. The most dominant solutions to such problems are knowledge-based approaches and the Minimax algorithm. The performance of these ap...

In this paper we study some results on Noetherian semigroups. We  show that if  $S_S$ is an  strongly  faithful $S$-act and $S$ is a duo weakly Noetherian, then we have the following.