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.
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equality between man and woman
Among Islamic law
International conventions and agreements
Objective(s): The present study aims at studying the relationship between immunoglobulin IgG, IgA,
IgM , as well as to C-3 and C-4 in brain tumours patients immunity (meningioms and gliomas).
Methodology: Forty sera of brain tumour patients were included 20 glioma and 20 meningioma was
tested to determine the levels of IgM, IgG IgA, C-3 and C-4 by using single radial immune-diffusion
technique and compared with 20 apparently healthy blood donors.
Results: The study revealed a significant decreasing in IgG levels in glioma as compare to meningioma
and control. The concentration of two other serum immunoglobulins and complement in both
meningioma and glioma show no significant differences with those in control group.
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This study includes replication and attenuation of foot and mouth disease virus type O which isolated from infected calves. Many passages for the virus in chick-Embryo were established as a substitute method to the tissue culture which is highly caustic in contrast to the chick embryo. The virus passed ten consequent passages which lead to the reduce of the titer of the virus from 106.53 TCID50/ 0.1 ml in cattle testis tissue culture to 103 TCID50/ 0.1 ml. the pathogenecity of attenuated FMD virus were also studied in both chick-embryo and guinea pigs. Using agar gel diffusion test precipitation antibodies was detected in guinea pig serum after 14 and 21 days post exposure to the attenuated virus. The inoculated guine
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The US invasion of Iraq in 2003 unleashed the repressed national aspirations of the Kurdish people. After the colonial powers, especially Britain, failed to establish a homeland of scattered Kurds in Iraq, Turkey, Syria and Iran, Iraq's Kurds managed to establish a semi-independent state in the north of the country Which lasted decades against the central authority in Baghdad in protest against what they call the forced integration of Kurds in the Iraqi state, and to obtain more rights and privileges as partners in this country. The federal region in the Kurdistan region of Iraq has become a reality, and it is eager not to strengthen its authority in return for the authority of the central government, but to annex other areas inhabited b
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