Let R be a commutative ring with identity and let Mbe a unitary R-module. We shall say that a proper submodule N of M is nearly S-primary (for short NS-primary), if whenever , , with implies that either or there exists a positive integer n, such that , where is the Jacobson radical of M. In this paper we give some new results of NS-primary submodule. Moreover some characterizations of these classes of submodules are obtained.
Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.
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
Back ground: In Iraq, after 2003 had more
accidents of the shell, bullet and stab abdominal
wounds, more over colon injuries.
Objective: The aim of this study is to evaluate
the most appropriate management of penetrating
colon injuries, comparing the primary repair with
the diversion.
Methods: Eighty patient series with shell, bullet
and stab colonic injuries during 4.5 years period
from June 2006-december 2010 at Al-Yarmouk
teaching hospital. The study compared the use of
primary repair versus diversion, analyzing
variables such as sex, age, severity of injury and
mortality rate.
Results: there were total 80 patients ,62 (77.5%)
male and 18(22.5%) female .male :female ratio
3.4:1. the most
Background: Insulin resistance is present in 50% or more of patients with primary hypothyroidism. Metformin can decrease TSH levels in these patients by a complex matter, this can be of great help in clinical practice.
Objective: This study was designed to evaluate the effect of metformin in reducing TSH levels in patients with primary hypothyroidism.
Methods: Hundred patients with primary hypothyroidism, 82 females, 18 males were included in this study, everyone was followed up for two months after adding metformin 850 mg twice daily in addition to thyroxin.
Results: 36 patients (36%) have a normal baseline TSH and no change after 2 months, 64 pa
... Show MoreLet R be a commutative ring with unity and let M be an R-module. In this paper we
study strongly (completely) hollow submodules and quasi-hollow submodules. We investigate
the basic properties of these submodules and the relationships between them. Also we study
the be behavior of these submodules under certain class of modules such as compultiplication,
distributive, multiplication and scalar modules. In part II we shall continue the study of these
submodules.
Let be a commutative ring with identity , and be a unitary (left) R-module. A proper submodule of is said to be quasi- small prime submodule , if whenever with and , then either or . In this paper ,we give a comprehensive study of quasi- small prime submodules.
In this notion we consider a generalization of the notion of a projective modules , defined using y-closed submodules . We show that for a module M = M1M2 . If M2 is M1 – y-closed projective , then for every y-closed submodule N of M with M = M1 + N , there exists a submodule M`of N such that M = M1M`.
Let R be an associative ring with identity and let M be a unitary left R–module. As a generalization of small submodule , we introduce Jacobson–small submodule (briefly J–small submodule ) . We state the main properties of J–small submodules and supplying examples and remarks for this concept . Several properties of these submodules are given . Also we introduce Jacobson–hollow modules ( briefly J–hollow ) . We give a characterization of J–hollow modules and gives conditions under which the direct sum of J–hollow modules is J–hollow . We define J–supplemented modules and some types of modules that are related to J–supplemented modules and int
... Show MoreA microbial contamination of several primary schools (official and private) in
Baghdad city was conducted. Sampling was performed in each school from desk,
door handle, and hand of students.
Out of 113swabs (classes desk, door holder, and students hands ) obtained from
ten primary schools, growth wasobserved in 91 samples (80.5%) (for official
school 84.6% and 71.4 for private school.
The results of recent study revealed that the official schools showed higher
contamination levels(130 CFU ) than private ones (90 CFU).
Resultes revealed that a total of 12 morphologically different bacterial species
were isolated from 62 bacterial isolates,among which gram negative bacteria 40
isolates(64.5%) were higher than