Ring theory is one of the influential branches of abstract algebra. In this field, many algebraic problems have been considered by mathematical researchers who are working in this field. However, some new concepts have been created and developed to present some algebraic structures with their properties. Rings with derivations have been studied fifty years ago, especially the relationships between the derivations and the structure of a ring. By using the notatin of derivation, many results have been obtained in the literature with different types of derivations. In this paper, the concept of the derivation theory of a ring has been considered. This study presented the definition of

     Ring theory is one of the influ

Four rapid, accurate and very simple derivative spectrophotometric techniques were developed for the quantitative determination of binary mixtures of estradiol (E2) and progesterone (PRG) formulated as a capsule. Method I is the first derivative zero-crossing technique, derivative amplitudes were detected at the zero-crossing wavelength of 239.27 and 292.51 nm for the quantification of estradiol and 249.19 nm for Progesterone. Method II is ratio subtraction, progesterone was determined at λmax 240 nm after subtraction of interference exerted by estradiol. Method III is modified amplitude subtraction, which was established using derivative spectroscopy and mathematical manipulations. Method IIII is the absorbance ratio technique, absorba

The Cu(II) was found using a quick and uncomplicated procedure that involved reacting it with a freshly synthesized ligand to create an orange complex that had an absorbance peak of 481.5 nm in an acidic solution. The best conditions for the formation of the complex were studied from the concentration of the ligand, medium, the eff ect of the addition sequence, the eff ect of temperature, and the time of complex formation. The results obtained are scatter plot extending from 0.1–9 ppm and a linear range from 0.1–7 ppm. Relative standard deviation (RSD%) for n = 8 is less than 0.5, recovery % (R%) within acceptable values, correlation coeffi cient (r) equal 0.9986, coeffi cient of determination (r2) equal to 0.9973, and percentage capita

A simple, accurate, precise, rapid, economical and a high sensitive spectrophotometric method has been developed for the determination of tadalafil in pharmaceutical preparations and industrial wastewater samples, which shows a maximum absorbance at 204 nm in 1:1 ethanol-water. Beer's law was obeyed in the range of 1-7?g/ mL ,with molar absorptivity and Sandell ? s sensitivity of 0.783x105l/mol.cm and 4.97 ng/cm2respectively, relative standard deviation of the method was less than 1.7%, and accuracy (average recovery %) was 100 ± 0. 13. The limits of detection and quantitation are 0.18 and 0.54 µg .ml-1, respectively. The method was successfully applied to the determination of tadalafil in some pharmaceutical formulations

Flow-injection (FI) spectrophotometric method has been developed for the analysis of thymol in pharmaceutical preparations. The method is based on organic coupling reaction between thymol and 4-amino antipyrine in the presence of alkaline medium to form an intense stable red color complex with copper nitrate that has a maximum absorption at 490 nm. Optimum conditions for determination of the drug was investigated .The calibration graph was linear over the range of 5-500 µg.ml-1 of thymol . The limit of detection (LOD) and limit of quantification (LOQ) were 1.81 ?g mL-1 and 3.60 ?g mL-1 respectively .The proposed method was applied satisfactorily to the determination of thymol in mouth wash preparations. The procedure is characterized by

A rapid, sensitive and without extraction spectrophotometric method for determination of clonazepam (CLO) in pure and pharmaceutical dosage forms has been described. The proposed method was simply depended on charge transfer reaction between reduced CLO (n-donor) and metol (N-methyl-p-aminophenol sulfate) as a chromogenic reagent (π- acceptor). The reduced drug, with zinc and concentrated hydrochloric acid, produced a purple colored soluble charge-transfer complex with metol in the presence of sodium metaperiodate in neutral medium, which has been measured at λmax 532 nm. All the variables which affected the developed and the stability of the colored product such as concentration of reagent and oxidant, temperature and time of rea

It is generally accepted that there are two spectrophotometric techniques for quantifying ceftazidime (CFT) in bulk medications and pharmaceutical formulations.  The methods  are described as simple, sensitive, selective, accurate and efficient techniques. The first method used an alkaline medium to convert ceftazidime to its diazonium salt, which is then combined with the 1-Naphthol (1-NPT) and 2-Naphthol (2-NPT) reagents. The azo dye that was produced brown  and red in color with absorption intensities of ƛmax 585 and 545nm respectively. Beer's law was followed in terms of concentration ranging from  (3-40) µg .ml^-1 For (CFT-1-NPT) and (CFT-2-NPT), the detection limits were 1.0096 and 0.8017 µg.ml^-1, respec

          Simple, cheap, sensitive, and accurate kinetic- spectrophotometric method has been developed for the determination of naringenin in pure and supplements formulations. The method is based on the formation of Prussian blue. The product dye exhibits a maximum absorbance at 707 nm. The calibration graph of naringenin was linear over the range 0.3 to 10 µg ml^-1 for the fixed time method (at 15 min) with a correlation coefficient (r) and percentage linearity (r²%) were of 0.9995 and 99.90 %, respectively, while the limit of detection LOD was 0.041 µg ml^-1. The method was successfully applied for the determination of naringenin in supplements with satisfac

This approach was developed to achieve an accurate, fast, economic and sensitivity to estimation of diphenhydramine Hydrochloride. The dye that produced via reaction between diphenhydramine HCl with thymol blue in acidic medium pH ≈ 4.0. The ion pair method include an optimization study to formed yellowcolored that extraction by liquid – liquid method. The product separated of complexes by using by chloroform solution measured spectrophotometry at 400 nm. The analysis data at optimum conditions showed that linearity concentration in a range of calibration curve 1.0 – 50 μg /mL, limit of detectionand limit of quantification 0.0786 and 0.2358 μg/mL respectively. The molar absorptivity and Sandell’s sensitivity were 1.8 × 10 -4 L/mo

In this study, four different spectrophotometric methods were applied for determination of cimetidine and erythromycin ethylsuccinate drugs in pure form and in their pharmaceutical preparations. The suggested methods are simple, sensitive, accurate, not time consuming and inexpensive. The results showed the following: The first method: Based on the formation of ion pair complex of each drug with bromothymol blue (BTB) as a chromogenic reagent. The formed complexes were extracted with chloroform and their absorbance values were measured at 427.5 nm for cimetidine and 416.5nm for erythromycin ethylsuccinate; against their reagents blanks. Two different methods, univariate method and multivariate method, were used to obtain the optimum condit