Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

As we live in the era of the fourth technological revolution, it has become necessary to use artificial intelligence to generate electric power through sustainable solar energy, especially in Iraq and what it has gone through in terms of crises and what it suffers from a severe shortage of electric power because of the wars and calamities it went through. During that period of time, its impact is still evident in all aspects of daily life experienced by Iraqis because of the remnants of wars, siege, terrorism, wrong policies ruling before and later, regional interventions and their consequences, such as the destruction of electric power stations and the population increase, which must be followed by an increase in electric power stations,

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       La traducción de los dos verbos ser y estar no es una tarea tan simple como piensan muchas personas, sino es una de las complicadas y difíciles tareas, ya que el traductor tiene que saber y perfeccionar los correctos casos gramaticales relacionados con esos dos verbos auxiliares  tanto el verbo ser como el verbo estar, especialmente en la frase nominal para que pueda dar una clara y correcta traducción. Usados con el mismo adjetivo, "ser" comunicará una cualidad que es parte de la identidad o naturaleza del sujeto, mientras que "estar" comunicará un estado o circunstancia del mismo. Este e

The main function of the auditing process is to get a financial report provide information about the activities of the economic entities. The financial report's information is intended to be useful in making decisions and planning for entities future. Such information became more effective and efficient if the auditors process analytical auditing procedures, by using those financial analysis tools, which mean more detailed indicators.

The objectives of this research are to investigate auditor's use of analytical procedures in Oman and identify the main objectives for using these procedures. A questionnaire was used to gather the data for the study. A sample of 65 auditors and the response rate was 80% (52).

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 This research aims to investigate the impact of a training program for teachers of chemistry according to the strategies for both sides of the brain together in academic achievement for their students, the sample consisted of a 12 teachers of both genders who are teaching chemistry for the students of the fifth scientific secondary schools of the General Directorate for the Education in Garmiyan/Sulaymaniyah governorate, Iraqi Kurdistan region, where five teachers of them randomly selected to involve the training program, and seven teachers did not participate in the proposed training program, where a sample of students was selected for each group of teachers about 147 male and female students for teachers of the experiment