The main goal of this paper is to give  a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of  purely hollow modules is considered.

A submodule Ϝ of an R-module Ε is called small in Ε if whenever  , for some submodule W of Ε , implies  . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if  , such that  , then  , where  is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .

Plagiarism Detection Systems play an important role in revealing instances of a plagiarism act, especially in the educational sector with scientific documents and papers. The idea of plagiarism is that when any content is copied without permission or citation from the author. To detect such activities, it is necessary to have extensive information about plagiarism forms and classes. Thanks to the developed tools and methods it is possible to reveal many types of plagiarism. The development of the Information and Communication Technologies (ICT) and the availability of the online scientific documents lead to the ease of access to these documents. With the availability of many software text editors, plagiarism detections becomes a critical

Research Summary

First: the problem of research and its importance

      The teacher's success in facilitating the students' learning and growth according to the educational and educational goals set out, he must identify the problems of discipline of students in the classroom in terms of sources and reasons and types and methods of prevention and treatment and the teacher to remember that success in his teaching and instruction is not completed more fully once he has the information And knowledge of the subject of the lesson, but must understand the dynamics of the group (class group) and master the skills of classroom management, su

Arabic calligraphy is one of the ancient arts rooted in history, And that he grew up conflicting views and writings addressed as a, communication tool for the linguistic The teaching calligraphy note an art and science because it depends on the fixed assets and precise rules in his art because centered Beauty It targets teach Arabic calligraphy speed as the education and recitation helps to write fast Which have great interest in the field of education and in life both Also accompanied Arabic calligraphy and scientific renaissance significant knowledge in the Ara

The subject of the tagged research (becoming and integration of the film in postmodern cinema) is summarized by studying the transformations and complementarity of the film in light of the emergence of the concern of postmodernism. Then the need for it, as well as the objectives of the research and clarify its limits, as well as its importance. Then the transition to the theoretical framework, which included two sections, the first topic was entitled: Postmodern Cinema Formation and Completion, while the second topic was entitled: Paradox in Postmodern Film.

After completing the theoretical aspect, the research concluded with a number of theoretical framework indicators that were adopted as a tool for analyzing the sample, then th

The concept of tolerance is gaining its importance in the midst of an international society suffering from violence, wars and internal and international crises. It is practiced by extremist and extremist forces and movements acting in the name of religion to exclude the different Muslim and non-Muslim people according to the unethical practices and methodologies of Islamic law and reality. , Cultural, civilization .. that distinguish our world today. The society today is suffering from the ideas of the intellectual and aesthetic views of the different ideologically, ethnically, culturally and religiously in the world of the South. This is what the end-of-history thesis of Fukuyama and the clash of civilizations represented to Huntington.

In this paper a new technique based on dynamic stream cipher algorithm is introduced. The mathematical model of dynamic stream cipher algorithm is based on the idea of changing the structure of the combined Linear Feedback Shift Registers (LFSR's) with each change in basic and message keys to get more complicated encryption algorithm, and this is done by use a bank of LFSR's stored in protected file and we select a collection of LFSR's randomly that are used in algorithm to generate the encryption (decryption) key.

We implement Basic Efficient Criteria on the suggested Key Generator (KG) to test the output key results. The results of applying BEC prove the robustness and efficiency of the proposed stream cipher cryptosystem.

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.