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ijs-7989
Strongly Essential Submodules and Modules with the se-CIP

     Let  be a ring with identity. Recall that a submodule  of a left -module  is called strongly essential if for any nonzero subset  of , there is  such that , i.e., . This paper introduces a class of submodules called se-closed, where a submodule  of  is called se-closed if it has no proper strongly essential extensions inside . We show by an example that the intersection of two se-closed submodules may not be se-closed. We say that a module  is have the se-Closed Intersection Property, briefly se-CIP, if the intersection of every two se-closed submodules of  is again se-closed in . Several characterizations are introduced and studied for each of these concepts. We prove for submodules  and  of  that a module  has the se-CIP if and only if  is strongly essential in  implies  is strongly essential in . Also, we verify that, a module  has the se-CIP if and only if for each se-closed submodule  of  and for all submodule  of ,  is se-closed in . Finally, some connections and examples are included about (se-CIP)-modules

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Publication Date
Mon Aug 26 2019
Journal Name
Iraqi Journal Of Science
On Weakly Second Submodules

    Let  be a non-zero right module over a ring  with identity. The weakly second submodules is studied in this paper. A non-zero submodule  of   is weakly second Submodule when  ,  where ,  and  is a submodule of  implies either  or   . Some connections between these modules and other related modules are investigated and number of conclusions  and characterizations are gained.

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Publication Date
Sun Oct 27 2019
Journal Name
Iraqi Journal Of Science
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Publication Date
Wed Nov 27 2019
Journal Name
Iraqi Journal Of Science
I-Nearly Prime Submodules

     Let  be a commutative ring with identity, and a fixed ideal of  and  be an unitary -module. In this paper we  introduce and study the concept of -nearly prime submodules as genrealizations of nearly prime and we investigate some properties of this class of submodules. Also, some characterizations of -nearly prime submodules will be given.

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Publication Date
Sun Dec 04 2011
Journal Name
Baghdad Science Journal
Approximate Regular Modules

There are two (non-equivalent) generalizations of Von Neuman regular rings to modules; one in the sense of Zelmanowize which is elementwise generalization, and the other in the sense of Fieldhowse. In this work, we introduced and studied the approximately regular modules, as well as many properties and characterizations are considered, also we study the relation between them by using approximately pointwise-projective modules.

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Publication Date
Thu Jul 01 2021
Journal Name
Iraqi Journal Of Science
Semi -T- Small Submodules

Let  be a ring with identity and  be a submodule of a left - module . A submodule  of  is called - small in  denoted by , in case for any submodule  of ,  implies .  Submodule  of  is called semi -T- small in , denoted by , provided for submodule  of ,  implies that . We studied this concept which is a generalization of the small submodules and obtained some related results

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Publication Date
Sun Jul 31 2022
Journal Name
Iraqi Journal Of Science
Small-Essentially Quasi-Dedekind R-Modules

In this research, we introduce a small essentially quasi−Dedekind R-module to generalize the term of an essentially quasi.−Dedekind R-module. We also give some of the basic properties and a number of examples that illustrate these properties.

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Publication Date
Sun Dec 02 2012
Journal Name
Baghdad Science Journal
Semi – Bounded Modules

Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

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Publication Date
Mon Jan 01 2001
Journal Name
Iraqi Journal Of Science
C.F Modules and C.P Modules

Let R be a commutative ring with identity. R is said to be P.P ring if every principle ideal of R is projective. Endo proved that R is P.P ring if and only if Rp is an integral domain for each prime ideal P of R and the total quotient ring Rs of R is regular. Also he proved that R is a semi-hereditary ring if and only if Rp is a valuation domain for each prime ideal P of R and the total quotient Rs of R is regular. , and we study some of properties of these modules. In this paper we study analogue of these results in C.F, C.P, F.G.F, F.G.P R-modules.

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Publication Date
Sun Apr 03 2005
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Serum Trace Elements ( Se+2, Cu+2, Zn+2) in Patients with Behcet's Disease

Background: Extensive reports denote the biological role of trace elements (Cu Zn ", Se ') in many various physiological and pathological conditions, one of the list is shown to be Behcet's disease (BD).The aim of this study was directed towards the distribution of trace elements (Cu 2,Zn, 2,Se 2) in sera of BD patients, and control groups.
Methods: Fifty Arab Iraqi patients who fulfdled the ISO criteria for diagnosis BD.compared with 21 patients control with recurrent oral ulcer (ROU), healthy control groups (2Ihealthy relative and 21healthy volunteer). Typing HLA Class I was carried out at Alkarama hospital, by using microlympho-cytotoxicity test. The concentrations of serum Cu ', Zn ", and Se" were determined by atomic absorption s

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Biosorption of Ciprofloxacin (CIP) using the Waste of Extraction Process of Microalgae: The Equilibrium Isotherm and Kinetic Study

       Scientists are investigating the efficacy of different biosorbents for promoting economic and environmental viability in purifying contaminants. Among the primary by-products of biodiesel production is waste microalgae biomass, which has the potential to be used as a cheap biosorbent for the treatment of pollution. In the present study, the biomass left over after extracting the chlorella vulgaris was used to test the potential biosorption of CIP from simulated aqueous solutions. Bisorbent's ability was characterized using Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDX). Analysis with a Fourier Transform Infrared Spectrometer revealed that C

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