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.
Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.
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The main goal of this paper is to introduce and study a new concept named d*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d*-supplement submodule. Many relationships of d*-supplemented modules are studied. Especially, we give characterizations of d*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d*-supplemented and by an example we show that the converse is not true.
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Astronomers have known since the invention of the telescope that atmospheric turbulence affects celestial images. So, in order to compensate for the atmospheric aberrations of the observed wavefront, an Adaptive Optics (AO) system has been introduced. The AO can be arranged into two systems: closedloop and open-loop systems. The aim of this paper is to model and compare the performance of both AO loop systems by using one of the most recent Adaptive Optics simulation tools, the Objected-Oriented Matlab Adaptive Optics (OOMAO). Then assess the performance of closed and open loop systems by their capabilities to compensate for wavefront aberrations and improve image quality, also their effect by the observed optical bands (near-infrared band
... Show MoreThe genic variation analysis of Pseudomonas aeruginosa after filtering the spurious variation appeared that 222 variable loci out of 5572 loci were detected. The type of variation analysis revealed that single nucleotide polymorphism was highly significant compared with other types of variation due the fact that the genome variation was achieved on the level of microevolution. Moreover, the proportional effect of functional scheme showed that genes responsible for environmental information were the highest comparable to another scheme. The genes of environmental information processing locate on outer membrane and face the defense strategy of the host therefore change in proteins coded by these genes lead to escape the immune system defense
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Objectives: to evaluate the role of conservative, decompression, spine fixation in management of closed spinal injury.
Methods: The study was conducted at Specialized Surgical hospital and Al-Kadhemayia Teaching Hospital, in the period between July 2003 and July 2005.The study included 61 patients categorized Into many groups according level of vertebral injury (cervical, cervicodorsal, dorsal, dorsolumbar, Lumbar and lumbosacral), type of injury (compressed fracture, burst fracture and fracture dislocation) And according the severity into three groups as G1( complete motor paralysis and sensory loss ) G2 ( complete motor paralysis and incomplete sensory loss) and G3 ( incomplete motor paralysis And incomplete sensory loss ).The metho
Our aim in this paper is to study the relationships between min-cs modules and some other known generalizations of cs-modules such as ECS-modules, P-extending modules and n-extending modules. Also we introduce and study the relationships between direct sum of mic-cs modules and mc-injectivity.
In this paper, the concept of semi-?-open set will be used to define a new kind of strongly connectedness on a topological subspace namely "semi-?-connectedness". Moreover, we prove that semi-?-connectedness property is a topological property and give an example to show that semi-?-connectedness property is not a hereditary property. Also, we prove thate semi-?-irresolute image of a semi-?-connected space is a semi-?-connected space.