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.
The current study was carried out at the Fields belongs of Horticulture Department, Collage of Agricultural Engineering Science, University of Baghdad, Al-Jadiriyah for the spring season 2016 -2017 to study the effect for inoculation mycorrhizae and folair application with bio stimulators and their interaction in the growth characters of (local okra ptera). A factorial experiment (2 in randomized complete block design (RCBD), the experiment included (12) treatment Distributed in three replicates. The three factors used in this experiment included . The inoculation with control (C) Mycorrhizae ( M ) , Biozyme (B ) ( B1 2cm3.L-1), ( B2 4cm1-.L-1) , Phosphalas (P) (P 2cm3.L-1), ( M + B1), ( M + B2), (P +
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Background: Diabetic mellitus type ? is a metabolic disorder of diverse etiological factors, characterized by hyperglycemia resulting from an absolute deficiency of insulin affected childhood and adolescent. Some of these patients seek an orthodontic care .The orthodontist who is treating these medically compromised patients should have a working knowledge of the multitude of medically complex problems. This information will support and enable for delivery of high standards of dental care in general and orthodontic care in particular. The aim of this study was to analyze serum IgG levels and salivary secretory IgA (sIgA) levels in human dentine extract (HDE) before (T0) and 6 months after (T6) orthodontic treatment and to correlate anti-HDE
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Background: The bond strength of root canal sealers to dentin was important for maintaining the integrity of the seal in root canal filling in both static and dynamic situations. In a static situation, it should eliminate any space that allowed the percolation of fluids between the filling and the wall while in a dynamic situation; it was needed to resist dislodgement of the filling during subsequent manipulation. Materials and Methods: Forty mandibular premolars were selected for this study. All canals were instrumented using ProTaper rotary instruments. Instrumentation was done with copious irrigation of 5.25% sodium hypochlorite. Roots were randomly divided into four groups according to the type of cleaning and method of root canal irrig
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Monetary policy occupies a prominent role in achieving monetary stability by adjusting the growth rates of the number of available means of payment in line with changes in the size of the gross domestic product in the country and expressed by the monetary stability coefficient agreed upon by the International Monetary Fund, a term that hides the fact that there is a rate of change in the volume of commodity or real production which expresses the levels of aggregate supply in the economy, which corresponds to the quantities of cash in circulation, which represent a net purchasing power and stimulate aggregate demand, which completes the picture of the existence of the market mechanism, expressed by the monetary or economic stability
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