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.
Background: Dyslipidemia is a major cause of
cardiovascular disease, which in turn, is the most
common cause of female morbidity and mortality.
Postmenopausal women (natural and surgical) are at
higher risk of developing cardiovascular disease,
especially coronary artery atherosclerosis.
Objective: To observe the relationship between blood
lipids: total cholesterol (TC), high density lipoproteincholesterol (HDL-C), low density lipoproteincholesterol (LDL-C), triglycerides (TGs), and very low
density lipoprotein- cholesterol (VLDL-C), LDL-C/
HDL-C ratio (atherogenic index) and menopausal
status, and to determine the co-factors that may explain
this relationship
Methods: A prospective, cross-sectional st
Purpose: The purpose of this study was to clarify the basic dimensions, which seeks to indestructible scenarios practices within the organization, as a final result from the use of this philosophy.
Methodology: The methodology that focuses adoption researchers to study survey of major literature that dealt with this subject in order to provide a conceptual theoretical conception of scenarios theory .
The most prominent findings: The only successful formulation of scenarios, when you reach the decision-maker's mind wa takes aim to form a correct mental models, which appear in the expansion of Perception managers, and adopted as the basis of the decisions taken. The strength l
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To track scientific developments and achievements, for example, that (achieved) after the Second World War until this moment, make each of us in absolute amazement. He invented the computer, discovered the genetic factor (DNA), and discovered the drawing of the human genetic map, going up to the moon, penetrating outer space by satellites, getting close to distant planets, producing jet planes, microprocessors, and lasers, in addition to enabling a person to create a layer of The material is extremely thin and extremely imaginative. It has also become possible for a person to "dig lines that do not exceed 20 billion meters of thickness." The human being was also able to collect things an atom and build an efficient and high-precision con
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It is no secret to anyone the lofty classifications and wonderful investigations made by Muslim scholars in various eras, with which they removed the dust of ignorance from the nation, clarified the argument, and illuminated the path of education, especially in the legal sciences, which are the foundation of religion.
It is the life of hearts and the path of grammarians in this world and the hereafter.
Among those scientific classifications are the investigations they have written in the science of the principles of legislation, which have established the general evidence and the original rules to which practical legal rulings are referred. And as you know, it is the basis of Islamic jurisprudence, a means of knowing its
... Show MoreThe aim of this research is to collect the semantically restricted vocabulary from linguistic vocabulary and make it regular in one wire with an in-depth study. This study is important in detecting the exact meanings of the language. On the genre, as shown in this research, and our purpose to reveal this phenomenon, where it shows the accuracy of Arabic in denoting the meanings, the research has overturned more than sixty-seven words we extracted from the stomachs of the glossaries and books of language, and God ask safety intent and payment of opinion.
The risks are considered as a large challenge facing the human communities. This challenge creates an economic and social burden which obstruct the community progress and influences on its evaluation in a negative way. In the last years, these risks began to increase and now it is necessary to face these risks in a regular and instructive methods in order to control over these risks and to limit its effects and reducing the losses, if it happened. The loss reduction and prevention programs produced by risks management are considered as a successful solution which enable to control these risks. These programs would not finish the danger in the community in a final way but it produces a practical solution reduces the negative effects and c
... Show MoreActive Learning And Creative Thinking
Background: Gingival recession is defined as the apical migration of the gingival margin below the cementoenamel junction (CEJ), resulting in exposure of the root surface and it is one of the main esthetic complaints of patients. The management of gingival recession and its sequelae is based on a thorough assessment of the etiological factors and the degree of tissue involvement.
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