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On J–Lifting Modules
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Abstract<p>Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if for every submodule N of M, there exists a submodule K of N such that <inline-formula> <tex-math><?CDATA ${\rm{M}} = {\rm{K}} \oplus \mathop {\rm{K}}\limits^\prime,\>\mathop {\rm{K}}\limits^\prime \subseteq {\rm{M}}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll"> <mrow> <mi mathvariant="normal">M</mi> <mo>=</mo> <mi mathvariant="normal">K</mi> <mo>⊕</mo> <mover> <mi mathvariant="normal">K</mi> <mo>′</mo> </mover> <mo>,</mo> <mi mathvariant="normal"> </mi> <mover> <mi mathvariant="normal">K</mi> <mo>′</mo> </mover> <mo>⊆</mo> <mi mathvariant="normal">M</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012025_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> and <inline-formula> <tex-math><?CDATA ${\rm{N}} \cap \mathop {\rm{K}}\limits^\prime { \ll _{\rm{J}}}\mathop {\rm{K}}\limits^\prime $?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi mathvariant="normal">N</mi> <mo>∩</mo> <mover> <mi mathvariant="normal">K</mi> <mo>′</mo> </mover> <msub> <mo>≪</mo> <mi mathvariant="normal">J</mi> </msub> <mover> <mi mathvariant="normal">K</mi> <mo>′</mo> </mover> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012025_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>. The am of this paper is to introduce properties of J–lifting modules. Especially, we give characterizations of J–lifting modules.We introduce J–coessential submodule as a generalization of coessential submodule . Finally, we give some conditions under which the quotient and direct sum of J–lifting modules is J–lifting.</p>
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Publication Date
Fri Dec 30 2011
Journal Name
Mustansiria Dental Journal
Effect of microwave irradiation on disinfection, dimensional accuracy, and surface porosity of dental casts
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To evaluate the effectiveness of different microwave irradiation exposure times on the disinfection of dental stone samples immersed in different solutions, and its affect on the dimensional accuracy and surface porosity. Dental stone casts were inoculated with an isolate of Bacillus subtilis to examine the efficiency of microwave irradiation as a disinfection method while immersed in different solutions; water, 40% sodium chloride, or without immersion for different durations. Dimensional accuracy and surface porosity were also evaluated. Significant reduction in colony counts of Bacillus subtilis were observed after 5 minutes of microwave irradiation of immersed dental casts in water and NaCl solution. No evidence of growth was observed a

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Publication Date
Thu Mar 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
The Impact of Intellectual trends on the nature of the Economic Structure of Iraq
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The Impact of Intellectual trends on the nature of the Economic Structure of Iraq

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Publication Date
Wed Jun 30 2010
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Study on Vanadium Recovery from Spent Catalyst Used in the Manufacture of Sulfuric Acid
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Spent catalysts for sulfuric acid production have large amount of vanadium and due to environmental authority it is required to reduce the vanadium contain of the spent catalyst. Experimental investigation was conducted to study the vanadium recovery from spent catalyst via leaching process using sodium hydroxide to study the effect of process variables (temperatures, sodium hydroxide molarities, leaching time and particle size) on vanadium recovery. The effect of process variables (temperature, particle size,molarities of sodium hydroxide and leaching time) on the percentages of vanadium recovery were investigated and discussed .It was found that the percentage of vanadium recovery increased with increasing temperature up to 100 , incre

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Publication Date
Wed Apr 01 2020
Journal Name
Plant Archives
Land cover change detection using satellite images based on modified spectral angle mapper method
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This research depends on the relationship between the reflected spectrum, the nature of each target, area and the percentage of its presence with other targets in the unity of the target area. The changes occur in Land cover have been detected for different years using satellite images based on the Modified Spectral Angle Mapper (MSAM) processing, where Landsat satellite images are utilized using two software programming (MATLAB 7.11 and ERDAS imagine 2014). The proposed supervised classification method (MSAM) using a MATLAB program with supervised classification method (Maximum likelihood Classifier) by ERDAS imagine have been used to get farthest precise results and detect environmental changes for periods. Despite using two classificatio

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Publication Date
Tue Dec 29 2020
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Preparation, Characterization and Optimization of Etoposide-Loaded Gold Nanoparticles Based on Chemical Reduction Method
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In recent years, observed focus greatly on gold nanoparticles synthesis due to its unique properties and tremendous applicability. In most of these researches, the citrate reduction method has been adopted. The aim of this study was to prepare and optimize monodisperse ultrafine particles by addition of reducing agent to gold salt, as a result of seed mediated growth mechanism. In this research, gold nanoparticles suspension (G) was prepared by traditional standard Turkevich method and optimized by studying different variables such as reactants concentrations, preparation temperature and stirring rate on controlling size and uniformity of nanoparticles through preparing twenty formulas (G1-G20). Subsequently, the selected formula that pr

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Publication Date
Thu Jun 01 2023
Journal Name
Iaes International Journal Of Artificial Intelligence (ij-ai)
Innovations in t-way test creation based on a hybrid hill climbing-greedy algorithm
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<p>In combinatorial testing development, the fabrication of covering arrays is the key challenge by the multiple aspects that influence it. A wide range of combinatorial problems can be solved using metaheuristic and greedy techniques. Combining the greedy technique utilizing a metaheuristic search technique like hill climbing (HC), can produce feasible results for combinatorial tests. Methods based on metaheuristics are used to deal with tuples that may be left after redundancy using greedy strategies; then the result utilization is assured to be near-optimal using a metaheuristic algorithm. As a result, the use of both greedy and HC algorithms in a single test generation system is a good candidate if constructed correctly. T

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Publication Date
Sat Jan 01 2022
Journal Name
Euphrates Journal Of Agricultural Science
Effect of potassium fertilization levels and organic nutrient on growth and yield of cucumber
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Publication Date
Wed Jan 01 2014
Journal Name
Journal Of The College Of Basic Education
Effect of annealing temperature on Structural and Optical properties of amorphous Selenium thin films
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Publication Date
Sat May 23 2026
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of chemotherapy on oral health status and salivary alkaline phosphatase among leukemic patients
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Background: Leukemia is a broad term given to a group of malignant diseases characterized by diffuse replacement of bone marrow with proliferating leukocyte precursors. Chemotherapy has been increasingly used to treat malignant conditions. The systemic sequelae as a result of these immunosuppressive techniques induce many oral and dental complications. This study was conducted to evaluate the effect of chemotherapy on oral health status and activity of salivary alkaline phosphates enzyme in patients with acute lymphocytic leukemia. Materials and methods: The study groups included 28 patients with acute lymphocytic leukemia; they were under chemotherapy, aged 20-25 year old. The control group includes healthy subjects matching with study

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Publication Date
Mon Apr 01 2019
Journal Name
Biochemical & Cellular Archives
The impact of follicular fluid growth differentiation factor 8 levels on IVF /ICSI outcomes
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Clinical index is needed to predict the outcome of pregnancy after in vitro fertilization/intracytoplasmic sperm injection-embryo transfer (IVF/ICSI-ET) for infertile patients. Growth differentiation factor-8 (GDF-8), also known as myostatin, is one of transforming growth factor-â superfamily localized in antral follicles in normal and PCOS ovaries but its function in female reproductive system is still unknown. Aim of the study is to assess the correlation between levels of GDF8 in follicular fluid (FF) with outcomes of in vitro fertilization (IVF/ICSI) in women with and without PCOS. A prospective case control study was performed enrolling (40) patients with PCOS and (40) non-PCOS women (male infertility) undergoing IVF/ICSI. The collect

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