An -module  is extending if every submodule of   is essential in a direct summand of . Following Clark, an -module  is purely extending if every submodule of   is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module     is Goldie extending if, for each submodule      of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module  is purely Goldie extending if, for each , there is a pure submodule P of such that  . Many c

A Module M is called cofinite  J- Supplemented  Module  if for every  cofinite submodule L of  M, there exists a submodule N of M such that M=L+N with   main properties of cof-J-supplemented modules.  An R-module M is called fully invariant-J-supplemented if for every fully invariant submodule N of M, there exists a submodule K of M, such that M = N + K with N  K K. A condition under which the direct sum of FI-J-supplemented modules is FI-J-supplemented was given. Also, some types of modules that are related to the FI-J-supplemented module were discussed.

 In this paper, we give a comprehensive study of min (max)-CS modules such as a closed submodule of min-CS module is min-CS. Amongst other results we show that a direct summand of min (max)-CS module is min (max)-CS module. One of interested theorems in this paper is, if R is a nonsingular ring then R is a max-CS ring if and only if R is a min-CS ring.

      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 M be ,-ring and X be ,M-module, Bresar and Vukman studied orthogonal
derivations on semiprime rings. Ashraf and Jamal defined the orthogonal derivations
on -rings M. This research defines and studies the concepts of orthogonal
derivation and orthogonal generalized derivations on ,M -Module X and introduces
the relation between the products of generalized derivations and orthogonality on
,M -module.

Our aim in this paper is to study the relationships between min-cs modules and some other known generalizations of cs-modules such as ECS-modules, P-extending modules and n-extending modules. Also we introduce and study the relationships between direct sum of mic-cs modules and mc-injectivity.

   Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXW for all fully invariant R-submodule X of M, implies XW.         M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.

Praise be to Allaah.
My research has included the following: The field of application of semantics when fundamentalists are the book and the Sunnah. Imam Ibn Hajar agreed with the majority of fundamentalists that what is meant from the year (one word denotes one side on two things onwards), and agreed that the significance of the year specific to the rest of its members is not a definite and definite formulas of the public has the singular known as (the) Astragharism, and the plural known as ( The nationality stating that dumping, pluralism is defined as (add), and nakra, if it occurs in the context of the condition, denial and prohibition, the names of the condition, the connected names, and the word (all - all). And the year in whic

Experimental study on the effect of cylindrical hollow cathode, working pressure and magnetic field on spatial glow distribution and the characteristics of plasma produced by dc discharge in Argon gas, were investigated by image analyses for the plume within the plasma. It was found that the emission intensity appears as a periodic structure with many peaks appeared between the electrodes. Increasing the pressure leads to increase the number of intensity peaks finally converted to continuous form at high pressure, especially with applied of magnetic field, i.e. the plasma is more stable with the presence of magnetic field. The emission intensity study of plasma showed that the intensity has a maximum value at 1.07 mbar pressure and decre