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.
Osteoporosis (OP) is a systemic skeletal disorder that is characterized by reduced bone mass and micro-architectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture. The most frequent osteoporotic fractures are fractures of the hip, wrist, and spine. The exact causes of OP are still unknown; several factors contribute to the disorder. Subjects and Methods: This study consists of patient groups, this group (Group A) was composed of 80 postmenopausal women with OP and osteopenia and the patient group was subdivided into two group; First group (GroupA1) was composed of 50 postmenopausal women with OP and the second group (Group A2) composed of (30) Postmenopausal Women with oste
... Show MorePraise be to Allah. Praise be to Him. We seek refuge in Him. We seek forgiveness from him. We seek forgiveness from him.
And the disadvantages of our actions, of his hands
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It is important, if not all, to pay tribute to God
Muhammad Abdo and Rasoulou, there is no way to deprive the nation of the weakness of God alone and not to share it
Which suffer from the Quran, and the loss of its borders, bad
The work did not work and did not improve
Do what they offer and delay the others, except by reference to this Koran and the extraction of treasures and secrets
And news.
The Great Quran Study
Lu Imito ordered each poisoned, and achieved several targets of
YEMYA: Knowing the secrets of the Grea
Two new nonsymmetrical mesogenic homologous series of terminal substituent ether (series [Vn]) and carboxy (series [VIn]) incorporating azobenzene and 1,3,4-oxadiazole group were synthesized. Both series have been All compounds thus isolated were purified and characterized by elemental analysis, Fourier Transform Infrared Spectroscopy, 1H NMR, along with thermal analysis and texture observation using Differential Scanning Calorimetry (DSC) and Polarizing Optical Microscopy (POM), respectively. All compounds of the first series exhibited liquid crystalline properties. The homologues [V1]-[V3] display a nematic mesophase, the compounds [V4]-[V7] exhibit a dimorphism behavior, nematic (N) and smectic A (SmA) mesophases, the compounds [V8] and
... Show MoreThis study came to show the importance of long hope and its extent on human life, and I found that through the research, the majority of the scholars did not address this topic separately, and did not explain the travails of this situation and the worldly problems it causes to its owner, and the consequences that fall upon it in the hereafter. Most of the studies inside of the books consisted of a simple presentation of this problem and an explanation of the remedies that came to us from the Qur'an and the hadiths and the Sunnah, and on the sayings of the imams of guidance (may the best prayers and peace be upon them), and on the chosen companions and followers, may God be pleased with them, but the length of hope does not stop At a certain
... Show MoreShatt Al-Diwaniya branches from Shatt Al-Hilla and extends for about 112 km until the Al-Rumaitha district within the study area located in Al-Diwaniya Governorate, Iraq. It is considered the main source for providing drinking water and supplying irrigation projects to the cities Al-Diwaniya and Al-Rumaitha. The study aims to evaluate, study, and develop Shatt Al-Diwaniya, as well as the new lined canal branching from Shatt Al-Diwaniya which. It is called Shatt Al-Diwaniya Diversion Canal. Field measurements of the discharge and water level were monitored, six sets for Shatt Al-Diwaniya and three sets for Diversion Canal. A one-dimensional model was developed by using HEC-RAS 5.0.7 so
Research in consumer science has proven that grocery shopping is a complex and distressing process. Further, the task of generating the grocery lists for the grocery shopping is always undervalued as the effort and time took to create and manage the grocery lists are unseen and unrecognized. Even though grocery lists represent consumers’ purchase intention, research pertaining the grocery lists does not get much attention from researchers; therefore, limited studies about the topic are found in the literature. Hence, this study aims at bridging the gap by designing and developing a mobile app (application) for creating and managing grocery lists using modern smartphones. Smartphones are pervasive and become a necessity for everyone tod
... Show MoreAnalysis system of sports players is very important for individuals in weightlifting. Assessment of player and strength is important for the performance of weightlifting. This paper proposes an analytical method for weightlifters with check-by-frame video. This analysis system can compute the major steps of seven positions in both snatch and clean and jerk methods in frame-video weightlifting monitoring of movements. Each user can compute the major steps of the seven positions of Hu moments among two frames in the video during training, and the Euclidian distance can be computed for the Hu moment values and lifting moment values in the snatch and clean and jerk methods during training. The outcome of the proposed system shows on efficien
... Show MoreThis work concerns the thermal and sound insulation as well as the mechanical properties of polymer matrix composite reinforced with glass fibers. These fibers may have dangerous effect during handling, for example the glass fibers might cause some damage to the eyes, lungs and even skin. For this reason the present work, investigates the behavior of polymer composite reinforced with natural fibers (Plant fibers) as replacement to glass fibers. Unsaturated Polyester resin was used as matrix material reinforced with two types of fibers, one of them is artificial (Glass fibers) and the other type is natural (Jute, Fronds Palm and Reed Fibers) by hand lay-up technique. All fibers are untreated with any chemical solvent. The Percentage of mi
... Show MoreThe removal of heavy metal ions from wastewater by sorptive flotation using Amberlite IR120 as a resin, and flotation column, was investigated. A combined two-stage process is proposed as an alternative of the heavy metals removal from aqueous solutions. The first stage is the sorption of heavy metals onto Amberlite IR120 followed by dispersed-air flotation. The sorption of metal ions on the resin, depending on contact time, pH, resin dosage, and initial metal concentration was studied in batch method .Various parameters such as pH, air flow rate, and surfactant concentration were investigated in the flotation stage. Sodium lauryl sulfate (SLS) and Hexadecyltrimethyl ammonium bromide (HTAB) were used as anionic and cationic surfactant re
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