doi:10.12988/IJA.2013.13011

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Publication Date

Tue Jan 01 2013

Journal Name

International Journal Of Algebra

Volume

7

DOI

10.12988/IJA.2013.13011

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Fully extending modules

Closed submodules

Quasi closed submodules

Extending modules

Fully extending modules

Strongly extending modules

Modules has SIP property

د.

...Show More Authors

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.

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Publication Date

Fri Jul 29 2022

Journal Name

Journal For Vascular Ultrasound

A Comparative Study of the Right and Left Carotid Arteries in Relation to Age for Patients With Diabetes and Hypertension

Introduction: Age

hypertension

and diabetes can cause significant alterations in arterial structure and function

including changes in lumen diameter (LD)

intimal-medial thickness (IMT)

flow velocities

and arterial compliance. These are also considered risk markers of atherosclerosis and cerebrovascular disease. A difference between right and left carotid artery blood flow and IMT has been reported by some researchers

and a difference in the incidence of nonlacunar stroke has been reported between the right and left brain hemispheres. The aim of this study was to determine whether there are differences between the right and left common carotid arteries and internal carotid arteries in patients with hypertension and diabetes for 2 age groups. Methods: We studied 250 patients with both diabetes and hypertension. Patients were divided into 2 age groups with the old age group being 56 to 75 years and the young age group 35 to 55 years. The bilateral common carotid and internal carotid arteries were evaluated with B-mode ultrasound and Doppler examinations. The LD and IMT were measured for both common carotid arteries

and spectral waveform parameters and indices were recorded for both internal carotid arteries. Results: The difference in LD between the left and right common carotid arteries for the old age group was 11.64% and for the young age group was 6.42%

with significant P values of <.05 for both age groups. The difference in IMT between the left and right common carotid arteries was 18.27% in the old age group compared with 15.38% in the young age group

with significant P values of <.05. There was a difference in peak systolic velocity between the left and right internal carotid arteries of 4.85% in the old age group which was not significant

compared with 14.28% in the young age group with a significant P value <.05

whereas the difference in end-diastolic velocity between the left and right internal carotid arteries was not significant for both age groups. Differences between the right and left internal carotid arteries for resistive index

pulsatility index

and pressure gradient were significant only in the young age group. Conclusion: We found significant differences between the right and left common carotid and internal carotid arteries in patients with diabetes and hypertension which were more prominent in the young age group. Values for common carotid IMT and LD were significantly higher in the left common carotid artery versus the right common carotid artery in both age groups. Differences between the 2 carotid sides may be attributed to anatomic variations in the common carotid artery origins which lead to differences in stress between the 2 sides

Ahmed Abduljabar

Samar I.

Anmar Z

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Introduction:

Age, hypertension, and diabetes can cause significant alterations in arterial structure and function, including changes in lumen diameter (LD), intimal-medial thickness (IMT), flow velocities, and arterial compliance. These are also considered risk markers of atherosclerosis and cerebrovascular disease. A difference between right and left carotid artery blood flow and IMT has been reported by some researchers, and a difference in the incidence of nonlacunar stroke has been reported between the right and left brain hemispheres. The aim of this study was to determine whether there are differences between the right and left common carotid arteries and internal carotid arteries in patient

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