Let R be an associative ring with identity and M be unital non zero R-module. A
submodule N of a module M is called a δ-small submodule of M (briefly N << M )if
N+X=M for any proper submodule X of M with M/X singular, we have
X=M .
In this work,we study the modules which satisfies the ascending chain condition
(a. c. c.) and descending chain condition (d. c. c.) on this kind of submodules .Then
we generalize this conditions into the rings , in the last section we get same results
on δ- supplement submodules and we discuss some of these results on this types of
submodules.
The existing investigation explains the consequence of irradiation of violet laser on the structure properties of MawsoniteCu6Fe2SnS8 [CFTS] thin films. The film was equipped by the utilization of semi-computerized spray pyrolysis technique (SCSPT), it is the first time that this technique is used in the preparation and irradiation using a laser. when the received films were processed by continuous red laser (700 nm) with power (>1000mW) for different laser irradiation time using different number of times a laser scan (0, 6, 9, 12, 15 and 18 times) with total irradiation time (0,30,45,60,75,90 min) respectively at room temperature.. The XRD diffraction gave polycrysta
... Show MoreThe dubbing process for the Foreign Dramas by the Kurdish language became a serious phenomenon in the Kurdish satellite TV, especially in the past few years. It attracted a wide audience, especially young adolescents. And prepared by some breakthrough hostile to Kurdish culture and value coordinated by others remedy for the structural gaps and lapses have, as a result of climate which is brought into existence globalization and secretions variety dimensional, saturated value and cognitive effects bearing a strong identity of its elements. From here, the problem of this research is the ambiguity of their role in a series of developmental processes Kurdish awareness of young people and the extent of the impact that caused it.
This
... Show MoreLet R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.
Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.
Throughout this paper R represents commutative ring with identity, and M is a unitary left R-module. The purpose of this paper is to study a new concept, (up to our knowledge), named a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.
Background:
Hepatitis C Virus is the main causative agent of hepatitis among blood transfused patients, in which most chronic cases result in liver carcinoma.
Materials & Methods:
Enzyme-Linked Immunosorbent Assay for HCV, FNF- and IL-12p40 estimation with Recombinant Immunoblotting Assay (RIBA) as a confirmatory test for HCV, have been
applied for HCV detection in 80 HCV patients' samples in comparison with 30 samples for apparently healthy control, while viral load has been estimated using Branched-DNA (b-
DNA) technique for 32 randomly selected positive cases for HCV. Liver function test has been applied for patients' sera in comparison with control.
Results & Conclusions:
This study re
Biosorption is an effective method to remove toxic metals from wastewaters. In this
study biosorption of lead and chromium ions from solution was studied using
Citrobacter freundii and Citrobacter kosari isolated from industrial wastewater. The
experimental results showed that optimum grwoth temperature for both bacteria is 30oC
and the optimum pH is 7 &6 for C. freundii and C. kosari respectively. While the
optimum incubation period to remove Pb and Cr for C. freundii and C. kosari is 4 days
and 3days respectively. Also the biosorption of Pb and Cr in mixed culture of bacteria
and mixed culture of Pb and Cr was investigated. Result indicate that uptake of Cr and
Pb for C.freundii, C. kosari and in mixes cultu
Biosorption is an effective method to remove toxic metals from wastewaters. In this
study biosorption of lead and chromium ions from solution was studied using
Citrobacter freundii and Citrobacter kosari isolated from industrial wastewater. The
experimental results showed that optimum grwoth temperature for both bacteria is 30oC
and the optimum pH is 7 &6 for C. freundii and C. kosari respectively. While the
optimum incubation period to remove Pb and Cr for C. freundii and C. kosari is 4 days
and 3days respectively. Also the biosorption of Pb and Cr in mixed culture of bacteria
and mixed culture of Pb and Cr was investigated. Result indicate that uptake of Cr and
Pb for C.freundii, C. kosari and in mixes cultu
The activation and reaction energies of the C-C and C-H bonds cleavage in pyrene molecule are calculated applying the Density Functional Theory and 6-311G Gaussian basis. Different values for the energies result for the different bonds, depending on the location of the bond and the structure of the corresponding transition states. The C-C bond cleavage reactions include H atom migration, in many cases, leading to the formation of CH2 groups and H-C≡C- acetylenic fragments. The activation energy values of the C-C reactions are greater than 190.00 kcal/mol for all bonds, those for the C-H bonds are greater than 160.00 kcal/mol. The reaction energy values for the C-C bonds range between 56.497 to 191.503 kcal/mol. As for the C-H cleavage rea
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