Let R be an associative ring. The essential purpose of the present paper is to introduce the concept of generalized commuting mapping of R. Let U be a non-empty subset of R, a mapping   : R  R is called a generalized commuting mapping on U if there exist a mapping :R R such that =0, holds for all U. Some results concerning the new concept are presented.

The ligand Schiff base [(E)-3-(2-hydroxy-5-methylbenzylideneamino)- 1- phenyl-1H-pyrazol-5(4H) –one] with some metals ion as Mn(II); Co(II); Ni(II); Cu(II); Cd(II) and Hg(II) complexes have been preparation and characterized on the basic of mass spectrum for L, elemental analyses, FTIR, electronic spectral, magnetic susceptibility, molar conductivity measurement and functions thermodynamic data study (∆H°, ∆S° and ∆G°). Results of conductivity indicated that all complexes were non electrolytes. Spectroscopy and other analytical studies reveal distorted octahedral geometry for all complexes. The antibacterial activity of the ligand and preparers metal complexes was also studied against gram and negative bacteria.

Diazotization reaction between quinolin-2-ol and (2-chloro-1-(4-(N-(5-methylisoxazol-3-yl)sulfamoyl)phenyl)-2l4-diazyn-1-ium was carried out resulting in ligand-HL, this in turn reacted with the next metal ions (Ni²⁺, Pt⁴⁺, Pd²⁺, and Mn²⁺)  forming stable complexes with unique geometries such as (tetrahedral for both Ni²⁺ and Mn²⁺, octahedral for Pt⁴⁺ and square planer for Pd²⁺ ). The creation of such complexes was detected by employing spectroscopic means involving ultraviolet-visible which proved the obtained geometries, fourier transfer proved the formation of azo group and the coordination with metal ion through it. Pyrolysis (TGA &

In this reserch Some new substituted and unsubstituted poly imides compounds. were synthesized by reaction of acrylol chloride with different amides (aliphatic and aromatic) in a suitable solvent in the presence amount triethyl amine (Et3N) with heating. The Structure confirmation of all polymers were confirmed using FT-IR,1H-NMR,13C-NMR and UV spectroscopy. Thermal analysis (TG) for some polymers showed their thermal stabilities. Other physical properties including softening points, melting point and solubility of the polymers were also measured

A range of macrocyclic dinuclear metal (II) dithiocarbamate-based complexes are reported. The preparation of complexes was accomplished from either mixing of the prepared ligand with a metal ion or through a template one-pot reaction. The preparation of the bisamine precursor was achieved through several synthetic steps. The free ligand; potassium 2,2'-(biphenyl-4,4'-diylbis(azanediyl))bis(1-chloro-2-oxoethane-2,1diyl)bis(cyclohexylcarbamodithioate) (L) was yielded from the addition of CS2 to a bis-amine precursor in  KOH medium.A variety of analytical and physical methods were implemented to characterise ligand and its complexes. The analyses were based on spectroscopic techniques (FTIR, UV-Vis, mass spectroscopy and 1H, 13C-NMR sp

Nilpotency of Centralizers in Prime Rings

In this paper we introduce and study the concepts of semisimple gamma modules , regular gamma modules and fully idempotent gamma modules as a generalization of semisimple ring. An module is called fully idempotent (semisimple , regular) if for all submodule of (every submodule is a direct summand, for each , there exists and such that . We study some properties and relationships between them.

In this paper we study necessary and sufficient conditions for a reverse- centralizer of a semiprime ring R to be orthogonal. We also prove that a reverse- centralizer T of a semiprime ring R having a commuting generalized inverse is orthogonal

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

In this paper, we introduce and study the notion of the maximal ideal graph of a commutative ring with identity. Let R be a commutative ring with identity. The maximal ideal graph of R, denoted by MG(R), is the undirected graph with vertex set, the set of non-trivial ideals of R, where two vertices I₁ and I₂ are adjacent if I₁ I₂ and I₁+I₂ is a maximal ideal of R. We explore some of the properties and characterizations of the graph.