Let  be a ring with identity and  be a submodule of a left - module . A submodule  of  is called - small in  denoted by , in case for any submodule  of ,  implies .  Submodule  of  is called semi -T- small in , denoted by , provided for submodule  of ,  implies that . We studied this concept which is a generalization of the small submodules and obtained some related results

      Fuchs introduced purely extending modules as a generalization of extending modules. Ahmed and Abbas gave another generalization for extending modules named semi-extending modules. In this paper, two generalizations of the extending modules are combined to give another generalization. This generalization is said to be almost semi-extending. In fact, the purely extending modules lies between the extending and almost semi-extending modules. We also show that an almost semi-extending module is a proper generalization of purely extending. In addition, various examples and important properties of this class of modules are given and considered. Another characterization of almost semi-extending modules is established. Moreover, the re

Let  be a commutative ring with identity and  be an -module. In this work, we present the concept of semi--maximal sumodule as a generalization of -maximal submodule.

We present that a submodule  of an -module  is a semi--maximal (sortly --max) submodule if  is a semisimple -module (where  is a submodule of ). We  investegate some properties of these kinds of modules.

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed

Objectives: to evaluate the role of conservative, decompression, spine fixation in management of closed spinal injury.
Methods: The study was conducted at Specialized Surgical hospital and Al-Kadhemayia Teaching Hospital, in the period between July 2003 and July 2005.The study included 61 patients categorized Into many groups according level of vertebral injury (cervical, cervicodorsal, dorsal, dorsolumbar, Lumbar and lumbosacral), type of injury (compressed fracture, burst fracture and fracture dislocation) And according the severity into three groups as G1( complete motor paralysis and sensory loss ) G2 ( complete motor paralysis and incomplete sensory loss) and G3 ( incomplete motor paralysis And incomplete sensory loss ).The metho

The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex

The topic of the research tagged (narrative structure and its impact on building open and closed endings in the fictional film) is summarized by studying the mechanism of employing closed and open endings in the fictional film. novelist, then the need for it, as well as the objectives of the research and clarifying its limits as well as its importance. Then moving to the theoretical framework, which included three topics, where the first topic was entitled (the cinematic construction of the film narrative), either the second topic (the structure of complexity and narrative solutions), or the third topic dealt with the subject (the structure of the end and its relationship to the construction of the narrative). After completing the theore

The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl

      Let  be a ring with identity and let  be a left R-module. If is  a proper submodule of  and  ,  is called --semi regular element in  , If there exists a decoposition  such that  is projective submodule of  and  . The aim of this paper is to introduce properties of F-J-semi regular module. In particular, its characterizations are given. Furthermore, we introduce the concepts of Jacobson hollow semi regular module and --semiregular module. Finally, many results of Jacobson hollow semi regular module and --semiregular module are presented.

    The main objective of this work is to generalize the concept of  fuzzy algebra by introducing the notion of  fuzzy algebra. Characterization and examples of the proposed generalization are presented, as well as several different properties of  fuzzy algebra are proven. Furthermore, the relationship between fuzzy algebra and fuzzy algebra is studied, where it is shown that the fuzzy algebra is a generalization of fuzzy algebra too. In addition, the notion of restriction, as an important property in the study of measure theory, is studied as well. Many properties of restriction of a nonempty family of fuzzy subsets of fuzzy power set are investigated and it is shown that the restriction of fuzzy algebra is fuzzy algebra too.