Group Ring Research Articles

Rings close to periodic with applications to matrix, endomorphism and group rings

We examine those matrix rings whose entries lie in periodic rings equipped with some additional properties. Specifically, we prove that the famous Diesl’s question whether or not a ring R being nil-clean implies that the matrix ring M n ( R ) over R is also nil-clean for all n ≥ 1 is paralleling to the corresponding implication for (abelian, local) periodic rings. Besides, we study when the endomorphism ring E ( G ) of an abelian group G is periodic. Concretely, we establish that E ( G ) is periodic exactly when G is finite as well as we find a complete necessary and sufficient condition when the endomorphism ring over an abelian group is strongly m-nil clean for some natural number m thus refining an “old” result concerning strongly nil-clean endomorphism rings. Responding to a question when a group ring is periodic, we show that if R is a right (resp., left) perfect periodic ring and G is a locally finite group, then the group ring RG is periodic, too. We finally find some criteria under certain conditions when the tensor product of two periodic algebras over a commutative ring is again periodic. In addition, some other sorts of rings very close to periodic rings, namely the so-called weakly periodic rings, are also investigated.

On Modules over G-sets

Let R be a commutative ring with unity, M a module over R and let S be a G–set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form ∑s∈Smss where ms∈M. The set MS is a module over the group ring RG under the addition and the scalar multiplication similar to the RG–module MG. With this notion, we not only generalize but also unify the theories of both of the group algebra and the group module, and we also establish some significant properties of (MS)RG. In particular, we describe a method for decomposing a given RG–module MS as a direct sum of RG–submodules. Furthermore, we prove the semisimplicity problem of (MS)RG with regard to the properties of MR, S and G.

Sugiol Masters Apoptotic Precision to Halt Gastric Cancer Cell Proliferation.

Sugiol, a natural compound with anticancer properties, has shown promise in various cancer types, but its potential in preventing gastric cancer remains uncertain. In this study, we aimed to examine the inhibitory effect of sugiol on human gastric cancer cell proliferation. Our findings demonstrate that sugiol effectively suppresses the proliferation of SNU-5 human gastric cancer cells, leading to apoptotic cell death. We assessed the chemo-preventive potential of sugiol via an MTT assay and confirmed the induction of oxidative stress using the H2DCFDA fluorescent dye. Treatment with sugiol at concentrations higher than 25 µM for 24 h resulted in an increase in intracellular levels of reactive oxygen species (ROS). This elevation of ROS levels inhibited cell-cycle progression and induced cell-cycle arrest at the G1 phase. Furthermore, our study revealed that sugiol reduces the viability and proliferation of SNU-5 cells in a dose-dependent manner. Importantly, ADME and toxicity analyses revealed that sugiol was effective and nontoxic at low doses. In parallel, we utilized the Swiss target prediction tool to identify potential targets for sugiol. Enzymes and nuclear receptors were identified as major targets. To gain insights into the molecular interactions, we performed structure-based molecular docking studies, focusing on the interaction between sugiol and STAT3. The docking results revealed strong binding interactions within the active site pocket of STAT3, with a binding affinity of -12.169 kcal/mole. Sugiol's -OH group, carbonyl group, and phenyl ring demonstrated hydrogen-bonding interactions with specific residues of the target protein, along with Vander Waals and hydrophobic interactions. These data suggest that sugiol has the potential to inhibit the phosphorylation of STAT3, which is known to play a crucial role in promoting the growth and survival of cancer cells. Targeting the dysregulated STAT3 signaling pathway holds promise as a therapeutic strategy for various human tumors. In combination with interventions that regulate cell cycle progression and mitigate the DNA damage response, the efficacy of these therapeutic approaches can be further enhanced. The findings from our study highlight the antiproliferative and apoptotic potential of sugiol against human gastric cancer cells (SNU-5). Moreover, the result underpins that sugiol's interactions with STAT3 may contribute to its inhibitory effects on cancer cell growth and proliferation. Further research is warranted to explore the full potential of sugiol as a therapeutic agent and its potential application in treating gastric cancer and other malignancies characterized by dysregulated STAT3 activity.

A reprogrammable mechanical metamaterial with origami functional-group transformation and ring reconfiguration

Recent advancements in reprogrammable metamaterials have enabled the development of intelligent matters with variable special properties in situ. These metamaterials employ intra-element physical reconfiguration and inter-element structural transformation. However, existing mono-characteristic homo-element mechanical metamaterials have limited reprogramming functions. Here, we introduce a reprogrammable mechanical metamaterial composed of origami elements with heterogeneous mechanical properties, which achieves various mechanical behavior patterns by functional group transformations and ring reconfigurations. Through the anisotropic assembly of two heterogeneous elements into a functional group, we enable mechanical behavior switching between positive and negative stiffness. The resulting polygonal ring exhibits rotational deformation, zero Poisson’s ratio stretching/compression deformation, and negative Poisson’s ratio auxetic deformation. Arranging these rings periodically yields homogeneous metamaterials. The reconfiguration of quadrilateral rings allows for continuous fine-tunability of the mechanical response and negative Poisson’s ratio. This mechanical metamaterial could provide a versatile material platform for reprogrammable mechanical computing, multi-purpose robots, transformable vehicles and architectures at different scales.

On the semisimplicity of twisted group rings and generalized Maschke’s theorem

Classical Maschke’s theorem gives a condition for the semisimplicity of group algebras over a field. As group algebras are a particular case of twisted group rings, we extend Maschke’s theorem to twisted group rings over division rings by proving that if the characteristic of a division ring [Formula: see text] does not divide the order of a finite group [Formula: see text], twisted group ring [Formula: see text] is semisimple. Then we prove the converse of this theorem for twisted group rings arising from split extensions of [Formula: see text] by [Formula: see text]. As there is a one-to-one correspondence between twisted group rings and group lattices over division rings, we conclude with the consequence of the semisimplicity of twisted group rings on group lattices.

Characterization of the unit group of ℤ[G × C2n

Let [Formula: see text] be a group and [Formula: see text] be the cyclic group of order 2. We characterize the unit group [Formula: see text] of the integral group ring [Formula: see text] in terms of the unit group [Formula: see text], for every positive integer [Formula: see text]. As a consequence, for each [Formula: see text], we determine conditions on some class of matrices [Formula: see text]s, to be in GL[Formula: see text]. Using this we calculate the integer solutions of some specific class of symmetric polynomial [Formula: see text] with integer coefficients.

Amenability problem for Thompson's group $F$: state of the art

This is a survey of our recent results on the amenability problem for Thompson's group $F$. They mostly concern esimating the density of finite subgraphs in Cayley graphs of $F$ for various systems of generators, and also equations in the group ring of $F$. We also discuss possible approaches to solve the problem in both directions.

DNA CODES FROM REVERSIBLE GROUP CODES BY A VIRUS OPTIMISATION ALGORITHM

In this paper, we employ group rings and some known results on group codes to study reversible group DNA codes. We define and study reversible cyclic DNA codes from a group ring point of view and we also introduce the notion for self-reciprocal group ring elements. Moreover, we search for reversible group DNA codes with the use of a virus optimisation algorithm. We obtain many good DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement and the fixed GC-content constraints.

Structural, physicochemical characterization and antimicrobial activities of a new tris(8-quinolinolato-κ2N,O)cobalt(III) ethanol solvate [Co(C9H6NO)3].(C2H6O)

We report herein the synthesis and physicochemical characterization of a new 8-hydroxyquinoline cobalt(III) complex ethanol solvate with formula [Co(C9H6NO)3].(C2H6O). This compound was been prepared by slow evaporation at room temperature and characterized by single crystal X-ray diffraction. It crystallizes in the monoclinic system, spaces group P21/n. The central cobalt ion has a slightly distorted square bipyramidal environment, coordinated by three chelating 8-hydroxyquinoline molecules. Structural cohesion is primarily established by π-π interactions between the neighboring rings of quinoline groups and intermolecular hydrogen bonds O-H…O connecting the cobalt complex entities and uncoordinated ethanol molecules.The title compound has been characterized by the infrared (IR) and the UV–Visible (UV–Vis) spectra. Intermolecular interactions in the crystal structure were quantified by Hirshfeld surface analysis. The band gap of the complex was calculated using solid-state reflectance spectra, and the results show that the complex acts as a semiconductor. Moreover, the new compound exhibits high antibacterial and antifungal activities, as detected by the well agar diffusion against various bacterial and fungal clinical strains. The superior inhibitory effect was observed against Klebsiella pneumoniae, Candida albicans and Candida glabrata with zones inhibition of about 17.5, 17.5 and 17 mm, respectively.

Radical Ring Opening Polymerization of Cyclic Ketene Acetals Derived From d-Glucal.

A cyclic ketene acetal (CKA) derived from d-glucal was synthesized, and its polymerization using free radicals has been investigated. NMR analysis of the resulting polymers revealed the formation of polyacetal-polyester copolymers, with up to 78% of ester linkages formed by radical ring-opening polymerization (rROP). Conversely, the polymerization of the monomer-saturated analogue only produced acetal linkages, demonstrating that the alkene functionality within the d-glucal pyranose ring is essential to promote ring-opening and ester formation, likely via the stabilization of an allyl radical. The thermal properties of the polymers were linked to the ratio of the ester and acetal linkages. Copolymerization with methyl methacrylate (MMA) afforded statistically PMMA-rich copolymers (66-98%) with linkages prone to hydrolytic degradation and decreased glass-transition temperatures. The retention of the pseudoglucal alkene function offers opportunities to functionalize further these bioderived (co)polymers.

Schatzki’s Ring in Asian Group of Patients

Schatzki's lower esophageal rings appear as thin membranous structures which do not contain any muscularis propria; resulting in a constricting ring at the esophagogastric junction, they are mostly asymptomatic. However, patients present with symptoms of dysphagia to solids and liquids and a sense of impaction of food. Diagnosis can be easily overlooked and can be confirmed by endoscopic inspection of the esophagogastric junction. 3 cases of Schatzki ring diagnosed on oesophagal endoscopy and its management are presented.

The diagonal coinvariant ring of a complex reflection group

The diagonal coinvariant ring of a complex reflection group

Synergistic Defect Passivation and Crystallization Modulation in Efficient Perovskite Solar Cells: The Case of Multifunctional 2-Anisidine-4-Sulfonic Acid.

With the continuous development of the performance of perovskite solar cells, the high-density defects on the perovskite film surface and grain boundaries as well as undesired perovskite crystallization are increasingly emerging as challenges to their commercial application. Herein, a dye intermediate 2-anisidine-4-sulfonic acid (2A4SA), containing sulfonic acid group (SO3-), amino group (-NH2), methoxy group (CH3O-), and benzene ring, which exhibit a synergistic effect in comprehensive defect passivation and crystallization modulation, is incorporated. Detailed investigations show that the SO3- of 2A4SA with high electronegativity firmly chelates with uncoordinated lead ions through the coordination interaction, while the -NH2 and the CH3O- of 2A4SA separately immobilize iodide ions and organic cations in the perovskite lattice through hydrogen bonds, enabling substantially decreased nonradiative recombination and trap state density. Meanwhile, 2A4SA molecules attached to the surface of perovskite nuclei can delay crystallization kinetics and promote preferred vertical growth orientation, thereby attaining the high-crystallinity and large-size-grain perovskite films. Consequently, the 2A4SA-doped device with the structure ITO/SnO2/Cs0.15FA0.75MA0.10PbI3 (2A4SA)/Spiro-OMeTAD/Ag presents a splendid power conversion efficiency (PCE) of 23.06% accompanied by increased open-circuit voltage (1.15 V) and fill factor (82.17%). Furthermore, the optimized film and device demonstrate enhanced long-term stability. The unencapsulated optimized device retains ≈80% of the original PCE after 1000 h upon exposure to ambient atmosphere (20-50% RH), whereas the control group is only 56.8%.

Application of pesticide application measures to reduce residue based on the metabolic transfer law of imidacloprid in banana leaves and soil

An investigation of the metabolism and transfer of imidacloprid (IMI) in banana plants and soil was performed using high-resolution mass spectrometry. Results indicated the presence of eight IMI metabolites in soil and leaves that resulted from hydroxylation of the imidazolidine ring, the reduction and loss of nitro groups, and oxidative cleavage of methylene bridges. Six metabolites, including 4/5-hydroxy IMI (4/5-hydroxy), IMI olefin (olefin), and 6-chloronicotinic acid (6-CNA), were detected in the fruits following leaf treatment, while only three were detected after soil treatment. Quantitative analysis showed that the total amount of imidacloprid and its metabolites transferred from leaves to fruits was higher than that transferred from soil to fruits. Therefore, leaf transfer was considered the main means by which IMI and its metabolites transferred to banana fruits. We found that adjuvants tank-mixed with IMI could reduce the total concentration of pesticide transfer from leaves to fruits, especially reducing the amount of metabolites transformed from the reduction and loss of nitro groups and oxidative cleavage of methylene bridges, thus reducing the pesticide residue in fruits and achieving the purpose of reducing the safety risk.

Synthesis and Antiphytopathogenic Activity of Novel Oxazolidine-2,4-diones Bearing Phenoxypyridine Moiety.

In the present study, we conducted optimization of pyramoxadone and synthesized a series of novel oxazolidinediones. Antifungal assays showed that these compounds exhibited moderate to excellent antifungal activity against various pathogens. Further SAR analysis revealed that the introduction of substituents to the benzene ring of the phenoxy group or the inclusion of bulky groups, such as tert-butyl, on the aniline moiety, had a detrimental effect on the activity. However, the inclusion of fluorine atoms in the aniline moiety significantly enhanced the antifungal efficacy. Notably, compound 2-4 displayed significantly higher activity compared to both pyramoxadone and famoxadone against R. solani, B. cinerea, S. sclerotiorum, and P. oryzae, where it demonstrated EC50 values of 1.78, 2.47, 2.33, and 2.23 μg/mL, respectively. Furthermore, compound 2-4 exhibited potent protective and curative effects against the tomato gray mold in vivo. A mechanistic investigation revealed that compound 2-4 significantly impacted the mycelial morphology, inhibited spore germination, and impeded mycelial respiration, ultimately leading to the inhibition of pathogenic fungus growth. These findings indicate that compound 2-4 has the potential to serve as a cyt bc1 inhibitor and should be further investigated for development.

Securing an Authenticated Privacy Preserving Protocol in a Group Signature Scheme Based on a Group Ring

Group signatures are a leading competing signature technique with a substantial amount of research. With group settings, group signatures provide user anonymity. Any group member with access to the group can generate a signature while remaining anonymous. The group manager, however, has the authority to expose and identify the signer if required. Since the privacy of the sender should be preserved, this is a conflict between privacy and accountability. Concerning high performance on security, we propose a novel, well-balanced security and privacy group signature scheme based on a general linear group over group ring. To the best of our knowledge, our work represents the first comprehensive framework for a group signature scheme that utilizes generic linear groups over group rings. We demonstrate that the competing security goals of message trustworthiness, privacy, and accountability are effectively resolved by our protocol. The results of the performance evaluation and simulation demonstrate that our protocol achieves strong security, system robustness, and high-performance efficiency, making it suitable for practical applications.

Weyl tensors, strongly regular graphs, multiplicative characters, and a quadratic matrix equation

We study solutions of a quadratic matrix equation arising in Riemannian geometry. Let S be a real symmetric n×n-matrix with zeros on the diagonal and let θ be a real number. We construct nonzero solutions (S,θ) of the set of quadratic equations∑kSi,k=0 and ∑kSi,kSk,j+Si,j2=θSi,j for i<j. Our solutions relate the equations to strongly regular graphs, to group rings, and to multiplicative characters of finite fields.

Matrix Representations of Endomorphism Rings for Torsion-Free Abelian Groups

Matrix Representations of Endomorphism Rings for Torsion-Free Abelian Groups

Idempotents in simple skew group rings and applications to skew cyclic codes

We give the form of complete sets of pairwise orthogonal primitive idempotents in a simple skew group ring. Using these idempotents, we construct some classes of skew cyclic codes. We give also some examples of MDS codes and rows orthogonal and MDS matrices. Communicated by Eric Jespers

Jordan Regular Units in Rings and Group Rings

Jordan Regular Units in Rings and Group Rings