Preferred Language
Details
Publication Date
Tue Oct 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Volume
33
Issue Number
4
DOI
10.30526/33.4.2513
Choose Citation Style
Statistics
View publication
6
Abstract Views
147
Galley Views
301
Statistics
Articles
/
jih-2513
Approximaitly Quasi-primary Submodules
: Prime submodules
Primary submodules
Socle of modules
Radical of submodules
Multiplication modules
Nonsingular modules.
Ali Sh. Ajeel
Omar A. Abdulla
Haibat K. Mohammadali
...Show More Authors

      In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left -module  over a commutative ring  with identity. This concept is a generalization of prime and primary submodules, where a proper submodule  of an -module  is called an approximaitly quasi-primary (for short App-qp) submodule of , if , for , , implies that either  or , for some . Many basic properties, examples and characterizations of this concept are introduced.

Crossref
View Publication Preview PDF
Quick Preview PDF
Related publications
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
...Show More Authors
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

 ... Show More
View Publication
Scopus (5)
Crossref (2)
Scopus Crossref