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: The role of prophylactic antibiotics remains controversial. It is clear that actively facial fractures are considered as clean contaminated and should be treated with therapeutic antibiotics; however, there is widespread variability in the use, type, timing, and duration of prophylactic antibiotic administrated in practice today. There is an adverse effect of increased antibiotic resistance, as well as costs, it is important to review the current evidence for the role of prophylactic antibiotics in compound facial fractures. The purpose of this study is to evaluate the role and significance of preoperative, perioperative and postoperative antibiotic prophylaxis for patients when there is already an infective focus, such as co
... Show MoreIntravascular embolisation of foreign bodies (FB) is a rare, serious complication that may occur during central venous line insertion. A 39-yearold male in a critical condition presented to casualty department with a through-and-through chest gunshot wound. Chest X-ray showed left haemothorax; an urgent chest tube was introduced and central venous access was introduced via the right femoral vein. The guided wire used in the procedure was unintentionally pushed to reach the right ventricular apex. Echocardiography confirmed FB location. Once stabilised, the patient was referred to Iraqi Centre of Cardiac Diseases, where transcatheter retrieval was performed. To stabilise the FB, a 6F pigtail catheter was used to create a U-shaped loop in the
... Show MoreLet R be a Г-ring, and σ, τ be two automorphisms of R. An additive mapping d from a Γ-ring R into itself is called a (σ,τ)-derivation on R if d(aαb) = d(a)α σ(b) + τ(a)αd(b), holds for all a,b ∈R and α∈Γ. d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]α = [a,b]α(σ,τ) holds for all a,b∈R and α∈Γ. In this paper, we investigate the commutativity of R by the strong commutativity preserving (σ,τ)-derivation d satisfied some properties, when R is prime and semi prime Г-ring.
Human resistin is an adipokine, with a possible link to coronary heart disease.A few studies were done about resistin in acute phase of ST-segment elevation myocardial infarction (STEMI) especially in Iraqi patients. Accordingly we design a study to investigate the association between resistin concentration and acute phase of STEMI in Iraqi patients.
The present study was carried out at Al-Yarmouk Teaching Hospital from December 2011 until June 2012. Serum resistin levels were measured in 50 patients with acute STEMI (mean age: 58.16 ± 11.73 years) at the first 12 hours of admission and 34 normal controls (mean age: 53.98 ± 15.46 years) matched for age, sex and other risk factors.
Resistin level in patients wi
... Show MoreThe research demonstrates new species of the games by applying separation axioms via sets, where the relationships between the various species that were specified and the strategy of winning and losing to any one of the players, and their relationship with the concepts of separation axioms via sets have been studied.
The significance of supra topological spaces as a subject of study cannot be overstated, as they represent a broader framework than traditional topological spaces. Numerous scholars have proposed extensions to supra open sets, including supra semi-open sets, supra delta-open sets and others. In this paper, the concept of supra delta-semi-open set was introduced within the generalizations of the supra topology of sets. Our investigation involves harnessing this category of sets to introduce new notions in these spaces, specifically supra delta-semi-limit points, supra delta-semi-derive points and examining their relationship with supra semi-open. Building upon this set classification, we introduce several additional concepts such as
... Show MoreThe x-ray fluorescence (XRF) of Znpc molecule with (flow of Ar) and Znpc molecule with (grow in N2) showed two peaks at (8.5and 9.5 Kv) referring to orbital transition ) K?-shell & K?-shell) respectively. The study of x-ray diffraction (XRD) where it was observed good growth of the crystal structure as a needle by the sublimation technique with a ?-phase of (monoclinic structure ) . Using Bragg equation the value of the interdistance of the crystalline plane (d-value) were calculated. We noticed good similarity with like once in the American Standards for Testing Material (ASTM) .Powder Diffraction File (PDF) Program was used to ensure the information obtained from (ASTM) . The output of (PDF) was compared with celn program, where the val
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