Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of M is called St-closed in M, if N has no proper semi-essential extension in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K, then N = K. We investigate the main properties of this type of submodules, and discuss some results that are useful in our work. The class of semi-extending modules is a generalization to the notion of extending modules, where an R-module M is called semi-extending, if every submodule of M is a semi-essential in a direct summand of M. Various properties of semi-extending modules are obtained, and we study the relationships between this class of modules and other related concepts.
The research in Islamic history is considered a title for the glory of the nation and a mirror for the intellectual and mental maturity of the men of the Islamic state who played an important role in saving humanity from darkness to light and from ignorance to knowledge and to show their position in building the Islamic state, and to highlight the importance of their conquests of neighboring cities and the expansion of Islam, and for this reason they appear The importance of writing on the topic (The Battle of Dumat al-Jandal and its impact on the era of the Prophethood and the Rightly Guided Caliphate). The reason for choosing this topic was to show the status of Dumat al-Jandal and its importance in the Islamic state and its great role
... Show MoreThe aim of the work is the synthesis and characterization of the tridentate Schiff base (HL) containing (N and O) as donor atoms type (ONO). The ligand is: (HL) phenyl 2-(2-hydroxybenzylidenamino)benzoate This ligand was prepared by the reaction of (phenyl 2-aminobenzoate) with salicylaldehyde under reflux in ethanol and few drops of glacial acetic acid which gave the ligand (HL). The prepared ligand was characterized by (FT IR,UV–Vis) spectroscopy, Elemental analysis of carbon, hydrogen and nitrogen (C.H.N.) and melting point. The ligand was reacted with some metal ions under reflux in ethanol with (1 metal :2 ligand )mole ratio which gave complexes of the general formula: Pr III , Cr and III La III [M(L)2]Cl , M = Products were found to
... Show MoreMetronidazole-MIPs were prepared by using (MDZ) as the template as well as allylchloride (AYC) or allylbromide (AYB) as monomer, used (TMPTA) tri-methylol propane tri-acrylate or ethylene glycol di-methyl acrylate (EGDMA) as cross-linker and initiator used (BP) benzyl peroxide. By using different plasticizers (di butyl Phthalate (DBPH), Nitrobenzene (NB), oleic acid (OA) and paraffin) for MDZ-MIP1 and (Di-butyl sebecate (DBS), Di-methyl acrylate (DMA), Tributylphosphate(TBP) and Tris(ethylhexyl phosphate (TEHP) ) for MDZ-MIP2. Membranes of MIPs were prepared in PVC matrix. The characterizations of each electrode were determined The Slope range from (55.083 - 43.711) mV/decade, Limit of Detection (8 X 10 -4- 2 X 10-6) and Linearity
... Show MoreNew Schiff-base ligands bearing tetrazole moiety and their polymeric metal complexes with Co(II), Ni(II) and Cd(II) ions are reported. Ligands were prepared in a multiple-step reaction. The reaction of sodium 2,6- diformylphenolate and cyclohexane-1,3-dione with 5-amino-2-fluorobenzonitrile resulted in the isolation of two precursors sodium 2,6-bis((E)-(3-cyano-4-fluorophenylimino)methyl)-4-methylphenolate 1 and 5,5'- (1E,1'E)-cyclohexane-1,3-diylidenebis- (azan-1-yl-1-ylidene)bis(2-fluorobenzonitrile) 2, respectively. The reaction of precursors with azide gave the required ligands; sodium 2,6-bis((E)-(4-fluoro-3-(1H-tetrazol-5- yl)phenylimino)methyl)-4-methylphenolate (NaL) and (N,N'E,N,N'E)-N,N'-(cyclohexane-1,3-diylidene)bis(4- fluoro-3-
... Show MoreFrom 211 urine samples, Gram negative bacteria were isolated from only 61 urine samples with isolation percentage 28.9%. Escherichia coli were isolated percentage 70.49% while Klebsiella pneumoniae and Psendomonas aeruginosa were 8.19% and 6.55%, respectively.Proteus spp. Were isolated from 9 (14.75%), P. mirablis and P. vulgaris were isolates percentage 11.47% and 3.27%, respectively. Uroepithelial Cell Adhesin (UCA) fimbriae expression by P.mirabilis isolates was detected by the high capacity to adhesion to human uroepithetial cells, the isolate p.mirabilis U7 was adhesion to human uroepithelial cells mean no.30.2 bacteria/cell when grown on luria broth at 37C for 24h, but then grown it’s on luria agar at 37C for 24h the adhesion
... Show MoreSome metal ions (Mn+2, Co+2, Ni+2, Cu+2, Zn+2, Cd+2 and Hg+2) complexes of quinaldic acid (QuinH) and α-picoline (α-Pic) have been synthesized and characterized on the basis of their , FTIR, (U.V-Vis) spectroscopy, conductivity measurements, magnetic susceptibility and atomic absorption. From the results obtained the following general formula has suggested for the prepared complexes [M(Quin)2( α-Pic)2].XH2O where M+2 = (Mn, Co, Ni, Cu, Zn, Cd and Hg), X = 2, X = zero for (Co+2 and Hg+2) complexes, (Quin-) = quinaldate ion, (α-Pic) = α-picoline. The results showed that the deprotonated ligand (QuinH) by using (KOH) coordinated to metal ions as bidentate ligand through the oxygen atom of the carboxylate group (-COO-) and the nitrogen ato
... Show Moreإحدى أهم الطرق لتقصي توزيع المجرات عبر الزمن الكوني هي دالة اللمعان LF بدلالة كتلة القرص الباريوني ψS(Mb)، القدر . لقد درسنا تقديرًا لكثافة كتلة الباريون في عينة من المجرات الحلزونية القضيبية وغير القضيبية من الادبيات السابقة، والتي تتضمن فعليًا، لكل صنف من الاجرام السماوية ذات المحتوى الباريون المرئي، جزءًا لا يتجزأ من ناتج دالة الضيائية (LF) ونسبة الكتلة إلى الضوء. استخدمت تقنية الانحدار المتعدد لحزمة الب
... Show More