The main goal of this paper is to introduce a new class in the category of modules. It is called quasi-invertibility monoform (briefly QI-monoform) modules. This class of modules is a generalization of monoform modules. Various properties and another characterization of QI-monoform modules are investigated. So, we prove that an R-module M is QI-monoform if and only if for each non-zero homomorphism f:M E(M), the kernel of this homomorphism is not quasi-invertible submodule of M. Moreover, the cases under which the QI-monoform module can be monoform are discussed. The relationships between QI-monoform and other related concepts such as semisimple, injective and multiplication modules are studied. We also show that they are proper subclass

      In this work, we introduced and studied  a new kind of soft mapping  on soft topological spaces with an ideal, which we called  soft strongly generalized mapping with respect an ideal I, we studied the concepts like SSIg-continuous, Contra-SSIg-continuous, SSIg-open, SSIg-closed and SSIg-irresolute mapping  and  the relations between these kinds of mappings and the composition of two mappings of the same type of two different types, with proofs or counter examples

  In this paper we introduced the concept of 2-pure submodules as a generalization of pure submodules, we study some of its basic properties and by using this concept we define the class of 2-regular modules, where an R-module M is called 2-regular module if every submodule is 2-pure submodule. Many results about this concept are given. 

This paper depends on sheding some litgt on the characteristics of political
relations between the arab and the Persian during the reign of sassane kings.
"Ardashir the first, shahbour the first, shahbour the second, Bahram the fifth; kisra
Anushrwan and kisrah abruis"
And who rulled the Persian before the Islamic conquest and were adopted in this studym
as a model. It was possible to get some information from invaluable refereces in order to
arrive at a clear image as regards the nature of these relations. These relations were
differently political according to the circumstances of ruling, interests and the personality
of those kings.

We introduce in this paper the concept of an approximately pure submodule as a     generalization of a pure submodule, that is defined by Anderson and Fuller. If every submodule of an R-module  is approximately pure, then  is called F-approximately regular. Further, many results about this concept are given.

Let be an associative ring with identity and let be a unitary left -module. Let  be a non-zero submodule of .We say that  is a semi- - hollow module if for every submodule  of  such that  is a semi- - small submodule ( ). In addition, we say that  is a semi- - lifting module if for every submodule  of , there exists a direct summand  of  and  such that  

The main purpose of this work was to develop the properties of these classes of module.

The research aims to achieve a set of objectives, the most important of which is determining the extent to which the auditors of the research sample in the Federal Bureau of Financial Supervision adhere to the requirements of the quality control system according to the Iraqi Audit Manual No. The federal financial / research sample with the quality control system according to the Iraqi audit guide No. 7), and the researcher seeks to test the main research hypothesis and sub-hypotheses, and to achieve this, a questionnaire was designed by (Google Form) and distributed electronically to the elements of the research sample, Through the statistical package program (SPSS), the results of the questionnaire were analysed. In light of the applied

The aim of this paper is to introduce and study the concept of SN-spaces via the notation of simply-open sets as well as to investigate their relationship to other topological spaces and give some of its properties.

        Throughout this paper, three concepts are introduced namely stable semisimple modules, stable t-semisimple modules and strongly stable t-semisimple. Many features co-related with these concepts are presented. Also many connections between these concepts are given. Moreover several relationships between these classes of modules and other co-related classes and other related concepts are introduced.

In this work , we study different chaotic properties of the product space on a one-step shift of a finite type, as well as other spaces. We prove that the product  is Lyapunove  â€“unstable if and only if at least one  or  is Lyapunove  â€“unstable. Also, we show that and locally everywhere onto (l.e.o)  if and only if is locally everywhere onto (l.e.o) .