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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 Sep 16 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Strongly Convergence of Two Iterations For a Common Fixed Point with an Application

     In this paper, we study some cases of a common fixed point theorem for classes of firmly nonexpansive and generalized nonexpansive maps. In addition, we establish that the Picard-Mann iteration is faster than Noor iteration and we used Noor iteration to find the solution of delay differential equation.

 

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Publication Date
Sat Apr 01 2023
Journal Name
Al-qadisiyah Journal Of Pure Science
Weakly and Strongly Forms of Fibrewise Fuzzy ω-Topological Spaces

This paper is devoted to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuzzy -ω-topological spaces, weakly fibrewise fuzzy -ω-topological spaces and strongly fibrewise fuzzy -ω- topological spaces. Also, Several characterizations and properties of this class are also given as well. Finally, we focused on studying the relationship between weakly fibrewise fuzzy -ω-topological spaces and strongly fibrewise fuzzy -ω-topological spaces.

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Publication Date
Thu Apr 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Extend Nearly Pseudo Quasi-2-Absorbing Submodules (II)

The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this concept and it is relationship to previous generalizationsm especially  2-Absorbing submodule and Quasi-2-Absorbing submodule, in addition to studying the most important Propositions, charactarizations and Examples. Now in this research, which is considered a continuation of the definition that was presented earlier, which is the Extend Nearly Pseudo Quasi-2-Absorbing submodules, we have completed the study of this concept in multiplication modules. And the relationship between the Extend Nearly Pseudo Quasi-2-Absorbing submodule and Extend Nearly Pseudo Quasi-2-Abs

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Iteration for a Non-Self -Strongly Pseudocontractive Map

Let be a Banach space, be a nonempty closed convex subset of , and be self
nonexpansive map. The sequence generated by the iterative method
, where be a contractive mapping
and is a sequence in We generalize the mapping to non-sel -Strongly
Pseudocontractive .

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Publication Date
Sun Feb 27 2022
Journal Name
Iraqi Journal Of Science
On Strong Dual Rickart Modules

    Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman studied Dual Rickart modules. The main purpose of this paper is to define strong dual Rickart module. Let M and N be R- modules , M is called N- strong dual Rickart module (or relatively sd-Rickart to N)which is  denoted by M it is N-sd- Rickart if for every submodule A of M and every homomorphism fHom (M , N) , f (A) is a direct summand of N. We prove that for an R- module M , if R is M-sd- Rickart , then every cyclic submodule of M is a direct summand . In particular, if M<

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Publication Date
Sun Jul 02 2023
Journal Name
Iraqi Journal Of Science
On δ-small M-Projective Modules

In this paper we study the concepts of δ-small M-projective module and δ-small M-pseudo projective Modules as a generalization of M-projective module and M-Pseudo Projective respectively and give some results.

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Publication Date
Sun Oct 22 2023
Journal Name
Iraqi Journal Of Science
On δ-small M-Projective Modules

In this paper we study the concepts of δ-small M-projective module and δ-small M-pseudo projective Modules as a generalization of M-projective module and M-Pseudo Projective respectively and give some results.

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Publication Date
Sun Apr 04 2010
Journal Name
Journal Of The Faculty Of Medicine Baghdad
The effect of Valsalva maneuver on diastolic filling indices in patients with essential hypertension.

Background: Left ventricular hypertrophy and diastolic dysfunction are considered to be an important risk factor for cardiovascular morbidity and mortality in asymptomatic hypertensive
patients. At the bedside, left ventricular geometric remodeling and diastolic dysfunction in hypertension can not be diagnosed without echocardiography which is a useful adjunct to the medical history, physical examination, ECG, and chest radiography. Hence, it provides an opportunity for good management and prognosis of what appears to be preclinical hypertensive complication. 
Subjects and Methods: 127 subjects with essential hypertension of either sex attending echo unit were subjected to medical history, clinical exa

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Publication Date
Sun Aug 01 2021
Journal Name
Journal Of Engineering Science And Technology
Green synthesis of iron nanoparticle using tea leave extract for removal ciprofloxacin (CIP) from aqueous medium

The approach of green synthesis of bio-sorbent has become simple alternatives to chemical synths as they use for example plant extracts, plus green synthesis outperforms chemical methods because it is environmentally friendly besides has wide applications in environmental remediation. This paper investigates the removal of ciprofloxacin (CIP) using green tea nano zero-valent iron (GT-NZVI) in an aqueous solution. The synthesized GT-NZVI was categorized using SEM, AFM, BET, FTIR, and Zeta potentials techniques. The spherical nanoparticles were found to be nano zero-valent, with an average size of 85 nm and a surface area of 2.19m2/g. The results showed that the removal efficiency of ciprofloxacin depends on the initial pH (2.5-10),

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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Semi-Small Compressible Modules and Semi-Small Retractable Modules

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

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