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.
Peer-Reviewed Journal
A low speed open circuit wind tunnel has been designed, manufactured and constructed at the
Mechanical Engineering Department at Baghdad University - College of Engineering. The work is one of
the pioneer projects adapted by the R & D Office at the Iraqi MOHESR. The present paper describes the
first part of the work; that is the design calculations, simulation and construction. It will be followed by a
second part that describes testing and calibration of the tunnel. The proposed wind tunnel has a test
section with cross sectional area of (0.7 x 0.7 m2) and length of (1.5 m). The maximum speed is about (70
m/s) with empty test section. The contraction ratio is (8.16). Three screens are used to minimize flow
distu
Human beings have an innate and natural aim to achieve their self-interests and to show their ability to overcome challenges in a better way, therefore the move towards self determination is expressed by intrinsic motivation. The desire of absorbing in this task is to enjoy the task in it self and benefitting from it such a motivation is the desire rooted in human nature to judge and choose in which individual is conscious in his self, abilities and adequacy that help him in control the different situations of life passed by him. His choices and actions are voluntary and non-restricted to intervention or external control because control is inner and subjective, while his behavior is self-regulated with the feeling of
... 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
Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe
... Show MoreTwo 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
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