Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings and modules.
The reaction of ethylenediamine with [2,4,6-trihydroxyacetophenon] and KOH (Schiff Base) to gives the new tetradentate ligand 2-(1-{2-{1-2,6-Dihydroxy-4-methyl phenyl)ethyliden amino}- ethylimino}-ethyl-benzene- 1,2,5-triol [HCl]. This ligand was reacted with some metal ions (Cu(II), Co(II), Ni(II), Zn(II), and Cd(II)) in methanol with (1:1) metal : ligand ratio to give a series of new complexes of the general formula [M(H4L)], where: M= Cu(11), Co(II), Ni(II), Zn(II), and Cd(II). All compounds were characterized by spectroscopic methods [I.R, U.V.-Vis, C.H.N., analysis H.P.L.C, atomic absorption, magnetic susceptibility, (EI-mass for the ligand)], and microanalysis along with conductivity measurements
... Show MoreEthylenediamine was reacted in the first step with 2,5 – hexandion to produce the precursor [A] , then [A] was reacted with diethylmalonate to give the new tetradentate macrocyclic Ligand [H2L].This Ligand was reacted with some metal ions in ethanol to give a series of new metal complexes of the general formula [M(HnL)X]m ( where : M= CrIII , n = 0 , X= Cl2 , m= -1 ; M = MnII , FeII , NiII , CuII , n = 1 , X= Cl2 , m = -1 ; M = CoII , n = 0 , X = Cl , m = -1 ; M = PdII , n = 0 , X=0 , m = 0 ; M = CdII , n = 2 , X = 0 , m = +2 . All compounds were characterize
... Show MoreAbstractOBJECTIVES: To evaluate the long-term remission efficacy and safety of isotretinoin in the treatment of Behcet's disease (BD). PATIENTS and METHODS: This single-blind, controlled therapeutic study was conducted in the Department of Dermatology and Venereology at Baghdad Teaching Hospital from February 2011 to January 2012. Thirty patients with BD were included in this work. Each patient received isotretinoin 20 mg orally once daily for 3 months. They were assessed at week 2 and then monthly depending on the Clinical Manifestation Index (CMI) and to record any side effects. At week 12, isotretinoin was stopped and patients were given placebo therapy in a form of glucose capsules for another 3 months. RESULTS: Thirty patients were tre
... Show MoreIn this paper we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of (denoted by ) Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.
In this paper, we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.
In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.
Throughout this paper we introduce the concept of quasi closed submodules which is weaker than the concept of closed submodules. By using this concept we define the class of fully extending modules, where an R-module M is called fully extending if every quasi closed submodule of M is a direct summand.This class of modules is stronger than the class of extending modules. Many results about this concept are given, also many relationships with other related concepts are introduced.
A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.
The spherical double pole-piece electron lens i§ depend on some
fact0rs : the- minimum va}ue-of projector fo·cal length (Fp)i:J,Iill • the
maximum value of magnetic flux density (Bm) , the total hal[ width
,(W) o'f asyriunetrical clln'e of magnetic field distribution [because there are differe_nt values of bore diameter (D1) • i. &
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