Let R be a commutative ring with 1 and M be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) Modules. We study s-essentially compressible (s-essentially retractable). We give some of their advantages, properties, characterizations and examples. We also study the relation between s-essentially compressible   (s-essentially retractable modules) and some classes of modules.

A simple and sensitive spectrophotometric method is described for the determination of diclofenac sodium (DCL), in pure form and pharmaceutical formulations. The method is based on the oxidation of 2,4-dinitrophenylhydrazine (2,4-DNPH) and coupling of the oxidized product with DCL in alkaline medium to give intensively colored chromogen which exhibits maximum absorption (λmax) at 600 nm, and the concentration of DCL was determined spectrophotometrically. The optimum reaction conditions and other analytical parameters were evaluated. In addition to classical univariate optimization, modified simplex method (MSM) has been applied in optimization of the variables affecting the color producing reaction. Beer’s law is obeyed in the

         A spectrophotometric reliable, rapid and sensitive method has been developed and validated for  the determination Ketotifen fumarate  . A method was described for the determination of Ketotifen Fumarate  in pure form or pharmaceutical formulations, a colored ion-pair complex formation reaction among ketotifen fumarate and acid-dye bromophenol blue at pH 3.0 was used for the colorimetric determination of the drug. The complex formed was extracted into chloroform and the maximum absorbance of the solution was measured at 413 nm against blank. The calibration curve calculated obey Beer's law over the concentration range of 0.4-16 μg/ml and the regression equation was A=0.069

A simple, accurate and sensitive spectrophotometric way is used to determine Bisacodyl in pure and pharmaceutical preparations. The proposed method depends on using 2,4-Dinitrophenylhydrazine as chromogenic reagent . The method was based on the oxidative coupling reaction of Bisacodyl with 2,4-Dinitrophenylhydrazine with Sodium periodate in the presence of sodium hydroxide as alkaline media to form red water soluble dye product , that has a maximum absorption at ?max 522nm . Beer ,s law is obeyed in the concentration of (2.00–20.00) ?g.ml -1 .The molar absorptivity is (6505) L.mol-1.cm-1,a sandall sensitivity of(0.0555) ?g.cm-2), correlation coefficient of (0.9970) , Limitof detection (LOD) (0.0312 ?g.ml-1), limit of Quantitation (LOQ) (

Simple and sensitive kinetic methods are developed for the determination of Paracetamol in pure form and in pharmaceutical preparations. The methods are based on direct reaction (oxidative-coupling reaction) of Paracetamol with o-cresol in the presence of sodium periodate in alkaline medium, to form an intense blue-water-soluble dye that is stable at room temperature, and was followed spectrophotometriclly at λmax= 612 nm. The reaction was studied kinetically by Initial rate and fixed time (at 25 minutes) methods, and the optimization of conditions were fixed. The calibration graphs for drug determination were linear in the concentration ranges (1-7 μg.ml-1) for the initial rate and (1-10 μg.ml-1) for the fixed time methods at 25 min.

In this study, the development of an indirect spectrophotometric method for the determination of folic acid in pure and pharmaceutical preparations is described. The method is based on the oxidation of pyrocatechol with iron (III) in an acidic medium, followed by the reaction with folic acid (FA) to produce a stable, water-soluble orange compound with maximum absorption at 350 nm versus the blank reagent. The complex of charge transfer was studied under optimal conditions; the titration graph was linear over the range of 0.5-25 μg/mL with a relative error of 1.2-2.8 and a relative standard deviation of 2.43-1.45 depending on the concentration level.

A new, Simple, sensitive and accurate spectrophotometric methods have been developed for the determination of sulfamethoxazole (SMZ) drug in pure and dosage forms. This method based on the reaction of sulfamethoxazole (SMZ) with 1,2-napthoquinone-4-sulphonic acid (NQS) to form Nalkylamono naphthoquinone by replacement of the sulphonate group of the naphthoquinone sulphonic acid by an amino group. The colored chromogen shows absorption maximum at 460 nm. The optimum conditions of condensation reaction forms were investigated by (1) univariable method, by optimizing the effect of experimental variables (different bases, reagent concentration, borax concentration and reaction time), (2) central composite design (CCD) including the effect of

A simple, precise, and sensitive spectrophotometric method has been established for the analysis of doxycycline. The method includes direct charge transfer complexation of doxycycline withp-Bromanil in acetonitrileto form a colored complex. The intensely colored product formed was quantified based on the absorption band at 377 nm under optimum condition. Beer’s law is obeyed in the concentration range of 1–50 μg.mL-1 with molar absorptivity of 1.5725x104 L.mol-1.cm-1, Sandell's sensitivity index (0.0283) μg.cm-2, detection limit of 0.1064 μg.mL-1, quantification limit 0.3224 μg.mL-1 and association constant of the formed complex (0.75x103). The developed method could find application in routine quality control of doxycycline and has

    Two different approaches, univariate and multivariate (simplex method), have been used to obtain the optimum conditions for the quantitative Spectrophotometric determination of Eu3+ using Solochrome violet RS (3-Hydroxy-4-(2-hydroxy phenyl azo) naphthalene -1sulfonic acid) (SVRS) as a chromogenic reagent. The investigation shows that Eu3+ ion forms a wine-red complex with SVRS in alkaline buffer solution having a maximum absorbance at 464 nm against reagent blank.       Calibration graphs obtained under univariate and simplex were found to be linear in the range of (0.30-8.0) µg/ml with detection limit 0.061µg/ml and molar absorptivity of 9877.66 L/mol.cm and (0.40-10.0)µg/ml with