Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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Let be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.

In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.

Background: Plane warts represent a common dermatological problem encountered in daily practice with no uniformly effective treatment modality.<br />Patients and methods: This study was conducted at the Department of Dermatology and Venereology of Baghdad Teaching Hospital / Medical City from April 2005 to June 2006. Fifty patients enrolled in the study and 36 completed it. Patients were instructed to apply isotretinoin gel once daily and keep on regular follow up every 2 weeks for one month to assess the esponse and side effects. At the end of the first month those with complete cure were instructed to stop therapy and keep on regular follow up to detect any recurrence.Patients with no response were divided into 2 groups. One grou

A simple indirect spectrophotometric method for determination of mebendazol in pure and pharmaceutical formulation was presented in this study. UV-Visible spectrophotometry using the optimal conditions was developed for determination of mebendazole in pure drug and different preparation samples. The method is based on the oxidation of drug by nbromosuccinimide with hydrochloric acid and the left amount of oxidizing agent was determined by the reaction with tartarazine and the absorbance was measured at 428 nm. Calibration curves were linear in the range of 5 to 30 µg.mL-1 with molar absorptivity 8437.2 L.mol-1 .cm-1 . The limits of detection and quantification were determined and found to be 0.7770 µg.mL-1 and 2.3400 µg.mL-1 respec

M(II) Ions using amino acid L- proline as a primary ligand and either Nicotinamide or 8- hydroxyqinoline as secondary ligand, respectively: a. The mixed ligand complexes of composition,[M(pro)2(na)2]. b. The mixed ligand complexes of composition , Na[M(pro)2(Q)]. Where proline (C5H9NO2) symbolized as pro H , Nicotinamide (C6H6N2O) symbolized as (NA) , 8- hydroxyqinoline, (C9H7NO2) symbolized as (8-HQ). The ligands and the metal chlorides were brought into reaction at room temperature (37ºc) in ethanol as solvent .The reaction required the following molar ratios [(1:2:2) metal:2NA:2pro-] and [(1:1:2) metal:Q:2pro-] with M+2 ions, where M = [Mn (II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and pd(II)]. Products were found to be solid crystall

 N-Pyridin-2-ylmethyl-benzene-1,2-diamine (L) was prepared from the reaction of ortho amino phenyl thiol with 2 – amino methyl pyridine in mole ratio (1:1) . It was characterized by elemental analysis (C.H.N) , FT-IR , Uv – Vis , 1H , 13C-N.M.R . The complexes of the bivalent ions (Co , Ni , Cu ,Pd , Cd , Hg and Pb) and the trivalent (Cr) have been prepared and characterized too . The structural was established by elemental analysis (C.H.N) , FT-IR , Uv – Vis spectra , conductivity measurements , atomic absorption and magnetic susceptibility . The complexes showed characteristic behavior of octahedral geometry around the metal ions and the (N,N,N) ligand coordinated in tridentat mode except with Pd complexes sho

The new ligand N-[2-(2-Phenyl hydrazinyl)Phenyl]benzothiazol-2-amine (L) was prepared from the reaction of orthoaminohydrazo benzene with 2-mercaptobenzothiazole in mole ratio (1:1). It was characterized by elemental analysis (CHN), 1H, 13C-NMR, IR and UV-Vis. The complexes of the bivalent ions Co(II), Ni(II), Cu(II), Cd(II), Hg(II) and Pb(II) have been prepared and characterized. The structural feature were established by elemental analysis (CHN), IR, UV-Vis spectra, conductivity measurements, atomic absorption and magnetic susceptibility. All complexes have been showed octahedral geometry except Cu(II) complex showed square planer. Dissociation degree, stability constant and molar absorptivity (l. mol-1. cm-1) were calculated for all c

The present work determines the particle size based only on the number of tracks detected in a cluster created by a hot particle on the CR-39 solid state nuclear track detector and depending on the exposure time. The mathematical model of the cross section developed here gives the relationship between alpha particle emitting from the (n, α) reaction and the number of tracks created and distribution of tracks created on the surface of the track detector. In an experiment performed during this work, disc of boron compound (boric acid or sodium tetraborate) of different weights were prepared and exposed to thermal neutron from the source. Chemical etching is processes of path formation in the detector, during which a suitable etching solut