The aim of this work is studying many concepts of a pure submodule related to sub-module L and introducing the two concepts, T_pure submodule related to submodule and the crossing property of T_pure related to submodule. Another characterizations and study some properties of this concept.
Let
Let
In this article, unless otherwise established, all rings are commutative with identity and all modules are unitary left R-module. We offer this concept of WN-prime as new generalization of weakly prime submodules. Some basic properties of weakly nearly prime submodules are given. Many characterizations, examples of this concept are stablished.
Let R be a commutative ring with identity and M be an unitary R-module. Let ï¤(M) be the set of all submodules of M, and ï¹: ï¤(M)  ï¤(M)  {ï¦} be a function. We say that a proper submodule P of M is ï¹-prime if for each r  R and x  M, if rx  P, then either x  P + ï¹(P) or r M ïƒ P + ï¹(P) . Some of the properties of this concept will be investigated. Some characterizations of ï¹-prime submodules will be given, and we show that under some assumptions prime submodules and ï¹-prime submodules are coincide.
The plant Zizyphus spina-christa grows wildly in the middle and southern of Iraq locally named Nabag. In this study the antibacterial activity of several different plant extract (alcoholic hot and cold extract 80%, aqueous hot and cold extract) was tested against some gram negative bacteria that related to Enterobacteriacea as follow; Pseudomonas aeruginosa, Escherchia coli Proteus mirabilis, Serratia mercesence,. Aeromonas sp, Klebsiella pneumoniae ,Shigella sp, Salmonella enteritidis (134), S. typhi(97), S. typhimurium (300) , S. typhi, . The results showed that efficient method of extract was alcoholic hot extract from other extract methods that are used in this study. The detection of active compound in crude extracts of the leaves show
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Background: During the pandemic, Corona virus forced many people, especially students, to spend more time than before on the computer and smartphone to study and communicate. The poor posture of the body may have worse effect on its body parts , most of which is the cervical spine (forward head posture). Objective: To assess the incidence of neck pain and the associated factors among undergraduate medical students related to position during E learning Subjects and Methods: Cross-sectional study was conducted among medical students in three Iraqi universities during 2021. The sample size w |
Several symptoms of hypothyroidism characterized by low
FT3 and FT4 were classified into hypothyroidism and Hoffman's syndrome .It was accepted that free radical generation and lipid peroxidation are associated with many diseases. Creatine kinase in serum is affected by thyroid hormones. This study was undertaken to investigate the relationship between malondialdehyde as a general lipid peroxidation marker and CK activity in patients with primary hypothyroidism and Hoffman's syndrome which indicatees hypothyroidism with undetectable FT3 and FT4 in serum with elevated values of TSH.
The study revealed that MDA is within the normal range, while CK activities in sera of Hoffman's syndrome were increas
... Show MoreBackground: During the pandemic, Corona virus forced many people, especially students, to spend more time than before on the computer and smartphone to study and communicate. The poor posture of the body may have worse effect on its body parts , most of which is the cervical spine (forward head posture). Objective: To assess the incidence of neck pain and the associated factors among undergraduate medical students related to position during E learning Subjects and Methods: Cross-sectional study was conducted among medical students in three Iraqi universities during 2021. The sample size was 152. Online questionnaire by Google forms sampling method were used to collect the data which was analysed using SPSS 25. Results: The perce
... 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 R be a commutative ring with identity and M an unitary R-module. Let ï¤(M) be the set of all submodules of M, and ï¹: ï¤(M)  ï¤(M)  {ï¦} be a function. We say that a proper submodule P of M is end-ï¹-prime if for each ï¡ ïƒŽ EndR(M) and x  M, if ï¡(x)  P, then either x  P + ï¹(P) or ï¡(M) ïƒ P + ï¹(P). Some of the properties of this concept will be investigated. Some characterizations of end-ï¹-prime submodules will be given, and we show that under some assumtions prime submodules and end-ï¹-prime submodules are coincide.