Let R be a commutative ring with unity .M an R-Module. M is called coprime module     (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M   In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.

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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The research includes the synthesis and identification of the mixed ligands complexes of M 2 Ions in general composition ,[M(Leu) 2 (SMX)] Where L leucine (C 6 H 13 NO 2 )symbolized (LeuH) as a primary ligand and Sulfamethoxazole C 10 H 11 N 3 O 3 S) symbolized (SMX)) as a secondary ligand . The ligands and the metal chlorides were brought in to reaction at room temperature in(v/v) ethanol /water as solvent containing NaOH. The reaction required the following [(metal: 2(Na Leu --): (SMX )] molar ratios with M(II) ions, Were M (  Mn ( II),Co (II),Ni(II),Cu( II),Zn (II),Cd(II)and Hg( The UV Vis and magnetic moment data revealed an octahedral geometry around M(II), The conductivity data show a non electrolytic nature of the complexes . The

In this paper, some series of new complexes of Mn(II), Co(II), Ni (II) Cu(II) and Hg(II) are prepared from the Schiff bases (L1,L2). (L1) derived from 4-aminoantipyrine and O-phenylene dia mine then (L2) derived from (L1) and 2-benzoyl benzoic acid. Structural features are obtained from their elemental microanalyses, molar conductance, IR, UV–Vis, 1H, 13CNMR spectra and magnetic susceptibility. The magnetic susceptibility and UV–Vis, IR spectral data of the ligand (L1) complexes get square–planar and tetrahedral geometries and the complexes oflig and (L2) get an octahedral geometry. Antimicrobial examinations show good results in the sharing complexes.

In this paper, some series of new complexes of Mn(II), Co(II), Ni (II) Cu(II) and Hg(II) are prepared from the Schiff bases (L1,L2). (L1) derived from 4-aminoantipyrine and O-phenylene dia mine then (L2) derived from (L1) and 2-benzoyl benzoic acid. Structural features are obtained from their elemental microanalyses, molar conductance, IR, UV–Vis, 1H, 13CNMR spectra and magnetic susceptibility. The magnetic susceptibility and UV–Vis, IR spectral data of the ligand (L1) complexes get square–planar and tetrahedral geometries and the complexes oflig and (L2) get an octahedral geometry. Antimicrobial examinations show good results in the sharing complexes.

  Let L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called  s- closed submodule denoted by  D ≤sc W, if D has   no  proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In  this  paper,  we study  modules which satisfies  the ascending chain  conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.

The research includes the synthesis and identification of the mixed ligands complexes of M+2ions in general composition[M(Asn)2(SMX)] Where L- Aspargine (C4H8N2O3)symbolized (AsnH) as a primary ligand and Sulfamethoxazole(C10H11N3O3S) symbolized (SMX) as a secondary ligand. The ligands and the metal chlorides were brought in to reaction at room temperature in(v/v) ethanol /water as solvent containing NaOH. The reaction required the following [(metal: 2(Na+Asn-): (SMX)] molar ratios with M(II) ions, Where: M(II)=Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II). The UV–Vis and magnetic moment data revealed an octahedral geometry around M(II), The conductivity data show a non-electrolytic nature of the complexes. The antimicrobial a

. New Schiff base ligand 2-((4-amino-5-(3, 4, 5-trimethoxybenzyl) pyrimidin2-ylimino) (phenyl)methyl)benzoic acid] = [HL] was synthesized using microwave irradiation trimethoprim and 2-benzoyl benzoic acid. Mixed ligand complexes of Mn((ІІ), Co(ІІ), Ni(ІІ), Cu(ІІ), Zn(ІІ) and Cd(ІІ) are reacted in ethanol with Schiff base ligand [HL] and 8-hydroxyquinoline [HQ] then reacted with metal salts in ethanol as a solvent in (1:1:1) ratio. The ligand [HL] is characterized by FTIR, UV-Vis, melting point, elemental microanalysis (C.H.N), 1H-NMR, 13C-NMR, and mass spectra. The mixed ligand complexes are characterized by infrared spectra, electronic spectra, (C.H.N), melting point, atomic absorption, molar conductance and magnetic m

The Co (II), Ni (II) ,Cu(II), Zn(II) ,Cd(II) and Hg(II) complexes of mixed of amino acid (L-Alanine ) and Trimethoprim antibiotic were synthesized. The complexes were characterized using melting point, conductivity measurement and determination the percentage of the metal in the complexes by flame (AAS). Magnetic susceptibility, Spectroscopic Method [FT-IR and UV-Vis]. The general formula have been given for the prepared mixed ligand complexes [M(Ala)2(TMP)(H2O)] where L- alanine (abbreviated as (Ala ) = (C5H9NO2) deprotonated primary ligand, L- Alanine ion .= (C5H8NO2-) Trimethoprim (abbreviated as (TMP ) = C10H11N3O3S M(II) = Co (II),Ni(II) ,Cu(II), Zn(II) ,Cd(II) and Hg(II). The results showed that the deprotonated L- Alanine b

The Co(II), Ni(II) ,Cu(II), Zn(II) ,Cd(II) and Hg(II) complexes of mixed of amino acid (L-Proline ) and Trimethoprim antibiotic were synthesized. The complexes were characterized using solubility, melting point, conductivity measurement ,. and determination the percentage of the metal in the complexes by flame(AAS).Magnetic susceptibility, Spectroscopic Method [FT-IR and UV-Vis]. Draw the proposed structure of the complexes using program , Chem. office 3D(2006). The ligands and there metal complexes were screened for their antimicrobial activity against four bacteria (gram + ve) and (gram -ve){Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus and Bacillus}.The proposed structure of the complexes using program , Chem office 3D(