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 aims to distinguish the reef environment from the non-reef environment. The Oligocene-Miocene-succussion in western Iraq was selected as a case study, represented by the reefal limestone facies of the Anah Formation (Late Oligocene) deposited in reef-back reef environments, dolomitic limestone of the Euphrates Formation (Early Miocene) deposited in open sea environments, and gypsiferous marly limestone of the Fatha Formation (Middle Miocene) deposited in a lagoonal environment. The content of the rare earth elements (REEs) (La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Er, Ho, Tm, Yb, Lu, and Y) in reef facies appear to be much lower than of those in the non-reef facies. The open sea facies have a low content of REEs due to bein
... Show MoreThe current research dealt with the symbolic significance and its effectiveness in the design of the industrial product, the aesthetic communicative discourse that embodies the imagination and human conscience. Whether according to what has been termed custom or what has been approved by traditions long ago, symbolism may be the main actor in linking the identifying components of the product. In addition, symbolism provides the user with the key to accessing a direct awareness of the product’s shape and function, as an identification of the product by stimulating the symbolic form of the consumer’s imagination and inviting him to To meditate in order to realize the implicit meaning behind these forms and thus achieve the symbolism of
... Show MorePhthalimide formation of Phthalic anhydride with various amines using microwave or without a method with the difference of the catalyst used in a prepared Phthalimide, either structure general are C6H4CONRCO and used as starting materials in synthesis several compounds derivative phthalimides are an important compounds because spectrum wide biological activities including Antimicrobial activity, anticonvulsant activity, Anti-inflammatory activity,Analgesic activity, Anti- influenza activity and Thromboxane inhibitory activity
The architecture of the richly decorated mosques demonstrated that the Islamic culture is one of the most significant and greatest civilizations in the history of humanity. The plant decorative units are one of the key areas in which the Muslim artist excelled. As a result, he created various plant forms that he took from nature, which led him to invent the arabesque art consisting of plant motifs with curved and rounded lines or wrapped between them. These shapes with curved borders include leaves, twigs, and flowers. Buildings and artefacts from the nineteenth century AD have this shape. they achieved their objectives during the twelfth and thirteenth centuries. There was another kind of vegetable decorative unit, made up of stems and
... Show MoreUrban growth of cities is connected with three related problems, the first one, is the deterioration of the center, which is a mark for historical origin. The second is the emergence of city edge, which contradicts by the center. The third one is the rapid semi urbanism of the edge. Literature review showed that Baghdad historical center (Old Rusafa and Karkh) had grown in four morphological stages, during which main paths had been changed from those which were perpendicular to the river front to those parallel to it. Research problem is that “there is a knowledge gap about the direction and origin of paths within Baghdad old center, after its growth”. The first research hypothesis is, “the direction of paths within old Baghdad cen
... Show MoreThis study was conducted to determine the side effects of dexamethasone n some physiological and immunological criteria, which included, Measuring sugar level, liver (ALT, AST , LDH, Total protein) and kidney function (urea, createnine), total and differential count of W.B.C,CRP, TNF-α ,IL6,IL10. thirty rats were divided into two groups (15\ rat). G1: This group was considered negative control injection with normal saline, G2: This group was injected with 2 mg\kg dexamethasone. The results showed a significant increase in the level of enzymesALT, AST and sugar levels and decreased level of total protein in the group treated with the drug, also showed, a significant decrease in the total number of W.B.C an
... Show More<span>Digital audio is required to transmit large sizes of audio information through the most common communication systems; in turn this leads to more challenges in both storage and archieving. In this paper, an efficient audio compressive scheme is proposed, it depends on combined transform coding scheme; it is consist of i) bi-orthogonal (tab 9/7) wavelet transform to decompose the audio signal into low & multi high sub-bands, ii) then the produced sub-bands passed through DCT to de-correlate the signal, iii) the product of the combined transform stage is passed through progressive hierarchical quantization, then traditional run-length encoding (RLE), iv) and finally LZW coding to generate the output mate bitstream.
... Show Morethis paper give a proof of known conditions for the existence of peridic conincidence points of continuius maps using lindemann theotem on transcendental numbers
The present article includes an experimental study of the behavior of dry and saturated dense sandy soil under the action of a single impulsive load. Dry and saturated dense sand models were tested under impact loads. Different falling masses from different heights were conducted using the falling weight deflectometer (FWD) to provide the single pulse energy. The responses of dense soils were evaluated at surface of soil under impact load. These responses include; displacements, velocities, and accelerations that are developed due to the impact acting at top and the displacement at different depths within the soil using the falling weight deflectometer (FWD) and accelerometers (ARH-500A waterproof, and low capacity acceleration tran
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