Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of M is called St-closed in M, if N has no proper semi-essential extension 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. We investigate the main properties of this type of submodules, and discuss some results that are useful in our work. The class of semi-extending modules is a generalization to the notion of extending modules, where an R-module M is called semi-extending, if every submodule of M is a semi-essential in a direct summand of M. Various properties of semi-extending modules are obtained, and we study the relationships between this class of modules and other related concepts.
Two field experiments were carried out for cultivating yellow maize crop Zea mays L. during the autumn planting season 2019 in two sites with soils of different textures. The first site is a loamy texture in one of the fields of the Medhatia Agriculture Division, Babylon Governorate. The second was silty loam by an alluvial mixture in one of the fields of Al-Nouriah Research Station, Ministry of Agriculture located in Al-Nouriah sub-district, Al-Qadisiyah governorate. It was found through the results that the uniformity, efficiency, and adequacy of the irrigation efficiency of the sprinkler irrigation method is better than that of the sprinkler irrigation method, and it ranged between (88.6-88.7) for uniformity and (84-86)% of the irrigatio
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In this study, the spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system ar
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Breast cancer (BC) is one of the most frequently observed malignancy in females worldwide. Today, tamoxifen (TAM) is considered as the highly effective therapy for treatment of breast tumors. Oxidative stress has implicated strongly in the pathophysiology of malignancies. This study aimed to investigate the changes in the levels of oxidants and antioxidants in patients with newly diagnosed and TAM-treated BC. Sixty newly diagnosed and 60 TAM-treated women with BC and 50 healthy volunteers were included in this study. Parameters including total oxidant capacity (TOC), total antioxidant capacity (TAC), and catalase (CAT) activity were determined before and after treatment with TAM. The serum levels of TOC and oxidative stress index (OSI) were
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Background: There are so many evidences that there was antimicrobial resistance, and there were many strains that emerged which were difficult to treat. We are living in a situation that the dissemination of multiple drug resistant bacteria can lead us to the situation, in which no treatment could be offered for bacterial infection in future.
Aim of study: Assessment of nurses’ knowledge, attitude, and practices on antibiotic use and resistance in Fatima Al Zahra hospital in Baghdad.
Subjects and Methods: A cross-sectional study. The study was carried on from 1st of February to 31st of March 2021. A questionnaire was constructed by the research team based on literature review and was adapted to asses
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