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.
This research is a study of the difficulties of learning the Arabic language that faces Arabic language learners in the Kurdistan Region, by revealing its types and forms, which can be classified into two categories:
The first type has difficulties related to the educational system, the source of which is the Arabic language itself, the Arabic teacher or the learner studying the Arabic language or the educational curriculum, i.e. educational materials, or the educational process, i.e. the method used in teaching.
The second type: general difficulties related to the political aspect, the source of which is the policy of the Kurdistan Regional Government in marginalizing the Arabic language and replacing the forefront of th
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Background: Periodontitis is an infection attributable to multiple infectious; it causes an interrelated cellular and humoral host immune responses. Recent reports have indicated that human cytomegalovirus (HCMV) may contribute to pathogenesis of periodontitis. The HCMV can stimulate the release of cytokines from inflammatory and non-inflammatory cells and weaken the periodontal immune defense. This study aimed to reveal the presence of anti-CMV IgG, and determine the levels of ILâ€6 and TNF-α and to correlate the presence of cytomegalovirus (CMV) with cytokines levels. Materials and Methods: Forty patients with chronic periodontitis and 40 healthy control subjects (their age and sex were matched with the patients) were involved
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Gaining the relationship between the central government and local governments is great importance especially after the expanded functions of the central government and became unable to carry out their works without all that delegate or transfer parts of its powers to lower levels.
The aims of the research is to determine the relationship of the central government with the local government in accordance with the principle of administrative decentralization with the presentation of the competent authorities, the control of local governments, according to the Provincial Council Act No. 21 of 2008 amended.
The research has a problem that has been the relationship of the central
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Inflammation of the tonsils could be described as acute tonsillitis, mainly due to infection. Recurrent tonsillitis could be defined as 3-7 episodes during the first 3 years of age. Vitamin D, which is a neuro-hormone with pleiotropic biological activities may modulate the immune response by alleviation, and stimulation of Th1 and Th2 cell proliferation, respectively, that influence the stimulation, synthesis, and secretion of both pro and anti-inflammatory cytokines. In this study we aimed to shed light on the levels of vitamin D in children with different episodes of tonsillitis in association with levels of interleukins (TNFα, IL-2, IL-4, IL-10). Blood samples were collected from 48 participants in 3 groups: control, acute tonsilliti
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Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n2), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ3) were e
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Pseudoephedrine (PSE) or (Sudafed) is one of the sympathomimetic group of drugs (ephedrine, PSE and amphetamines) which effects cardiovascular system, respiratory system, and gastrointestinal tract. However, only little researches had supported its effect on solid abdominal organs. This study aims to investigate the effects of different doses of Sudafed in the liver and kidney of albino mice. The current study included 18 albino mice grouped into 2 groups: control (3 mice), and acute group (15 mice). The acute group was further subdivided into 5 subgroups, each subgroup of 3mice wasgiven a lonely intaperitonial injection of 0.3ml of the following conc. (500mg/kg, 250mg/kg, 125mg/kg, 62.52mg/kg, and 31.24mg/kg) for 24hrs. After the m
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