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.
In this paper, I highlight the bishops mentioned in the Bible in its sections
(The Old and New Testaments) where these books still retain the remaining remnant of the Bible
Issuing the prophets who preceded the mission of the Prophet Muhammad (peace and blessings of Allaah be upon him) and they must pray
And peace, as those bishops were mentioned in the Book of Formation through the recitation of the psalms
To Habakkuk, Malakhi, and Hajji.
As well as in the New Testament, which we see clearly in the four Angels: Matthew, Luke,
Disco, John.
Then the male lamented what was said of those bishops by expressing the eternal heavenly book (the Qur'an)
Al - Karim) as he focuses on this subject from multiple angles and exp
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This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.
The US invasion of Iraq in 2003 unleashed the repressed national aspirations of the Kurdish people. After the colonial powers, especially Britain, failed to establish a homeland of scattered Kurds in Iraq, Turkey, Syria and Iran, Iraq's Kurds managed to establish a semi-independent state in the north of the country Which lasted decades against the central authority in Baghdad in protest against what they call the forced integration of Kurds in the Iraqi state, and to obtain more rights and privileges as partners in this country. The federal region in the Kurdistan region of Iraq has become a reality, and it is eager not to strengthen its authority in return for the authority of the central government, but to annex other areas inhabited b
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Adsorption studies were performed at different initial Tetracycline (TC) and Amoxicillin (AMO) concentration, different biomass dosage and type, contact time, agitation speed, and initial pH. In the batch mode were investigated. The optimum pH of solutions is 6.5 for TC and 5 for AMO, agitation speed 200 rpm and concentration 50 ppm. The results in FTIR showed that there were -OH and amides (N-H) and other functional groups on the surface of Cladophora and Spirulina algae. The equilibrium isotherm data were modeled with Freundlich, Temkin, and Langmuir isotherm models. The data best fitted with the Langmuir model. The maximal adsorption capacity from the Langmuir model was (9.86, 20. 5 mg/g) for TC and (7.89, 17.4 mg/g) for AMO on
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Nowadays, a strong relationship between the agriculture sectors and digital technologies is really interesting. The article describes how recent intelligent technologies can improve agricultural fields. Mobile applications are software programs created on smartphones, tablets, and computers. Agricultural fields mainly represent the pillar of the economy and the business sector that fulfills the world's food requirements. The United States has a valuable rank in potato production, which depends on this production economically.
Nevertheless, so many insects affect potato yield production quantitatively and qualitatively. So, a smartphone App was created to help potato growers diagnose insects that directly attack potato cro
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