In this paper, the concept of fully stable Banach Algebra modules relative to an ideal has been introduced. Let A be an algebra, X is called fully stable Banach A-module relative to ideal K of A, if for every submodule Y of X and for each multiplier ?:Y?X such that ?(Y)?Y+KX. Their properties and other characterizations for this concept have been studied.

Chapter-1

Problem of the research: 

The studies and researches have noticed the aggravation of violence practice in all educational means using different and innovated styles against children in the school and house in order to upbringing by the parents or the school .

It is a training method for the person to participate in the society and prepare him to be an effective member.

The current research confines the children in age (6-12) years old representing the primary stage who face different kind of violence during the familiar or school education.

The current research aims to:

1 – The kinds of violence which happens to the children in the primary

A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.

        Let R be a commutative ring with unity. In this paper we introduce the notion of chained fuzzy modules as a generalization of chained modules. We investigate several characterizations and properties of this concept

Throughout this paper we introduce the concept of quasi closed submodules which is weaker than the concept of closed submodules. By using this concept we define the class of fully extending modules, where an R-module M is called fully extending if every quasi closed submodule of M is a direct summand.This class of modules is stronger than the class of extending modules. Many results about this concept are given, also many relationships with other related concepts are introduced.

Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called special selfgenerator or weak multiplication module if for each cyclic submodule Ra of M (equivalently, for each submodule N of M) there exists a family {fi} of endomorphism of M such that Ra = ∑_i▒f_i (M) (equivalently N = ∑_i▒f_i (M)). In this paper we introduce a class of modules properly contained in selfgenerator modules called special selfgenerator modules, and we study some of properties of these modules.