Throughout this paper R represents commutative ring with identity, and M is a unitary left R-module. The purpose of this paper is to study a new concept, (up to our knowledge), named a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.

Let  be a commutative ring with 1 and  be a left unitary . In this paper, the generalizations for the notions of compressible module and  retractable module are given.

An   is termed to be  semi-essentially compressible if   can be embedded in every of a non-zero semi-essential submodules. An  is termed a semi-essentially retractable module, if   for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given.  We also study the relation between these classes and some other classes of modules.

Volleyball is one of the sports that require physical and skill abilities thus many teaching models appeared to teach these abilities like group investigation model. The research aimed at identifying the effect of group investigation model on learning underarm and overhead passing in volleyball. The researchers hypothesized statistical differences between pre and posttests in learning underarm and overhead passing in volleyball as well as differences in posttests of controlling and experimental groups in learning underarm and overhead passing in volleyball. The researcher used the experimental method on (30) second year female students of physical education and sport sciences college/ university of Baghdad. Group investigation model was app

In this paper we introduced a new class of - called - and study their basic properties in nano topological spaces. We also introduce -closure and -interior and study some of their fundamental properties.

The main objective of this paper is to find the order and its exponent, the general form of all conjugacy classes, Artin characters table and Artin exponent for the group of lower unitriangular matrices L(3,? p ), where  p  is prime number.

The notion of a Tˉ-pure sub-act and so Tˉ-pure sub-act relative to sub-act are introduced. Some properties of these concepts have been studied.

Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio