In this paper we give many connections between essentially quasi-Dedekind (quasi-
Dedekind) modules and other modules such that Baer modules, retractable modules,
essentially retractable modules, compressible modules and essentially compressible
modules where an R-module M is called essentially quasi-Dedekind (resp. quasi-
Dedekind) if, Hom(M N ,M )  0 for all N ≤e M (resp. N ≤ M). Equivalently, a
module M is essentially quasi-Dedekind (resp. quasi-Dedekind) if, for each
f End (M) R  , Kerf ≤ e M implies f = 0 (resp. f  0 implies ker f  0 ).

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

A class of hyperrings known as divisible hyperrings will be studied in this paper. It will be presented as each element in this hyperring is a divisible element. Also shows the relationship between the Jacobsen Radical, and the set of invertible elements and gets some results, and linked these results with the divisible hyperring. After going through the concept of divisible hypermodule that presented 2017, later in 2022, the concept of the divisible hyperring will be related to the concept of division hyperring, where each division hyperring is divisible and the converse is achieved under conditions that will be explained in the theorem 3.14. At the end of this paper, it will be clear that the goal of this paper is to study the concept

The structure of this paper includes an introduction to the definition of the nano topological space, which was defined by M. L. Thivagar, who defined the lower approximation of G and the upper approximation of G, as well as defined the boundary region of G and some other important definitions that were mentioned in this paper with giving some theories on this subject. Some examples of defining nano perfect mappings are presented along with some basic theories. Also, some basic definitions were presented that form the focus of this paper, including the definition of nano  pseudometrizable space, the definition of nano compactly generated space, and the definition of completely nano para-compact. In this paper, we presented images of nan

    In this paper, some new types of regularity axioms, namely pairwise quasi-regular, pairwise semi-regular, pairwise pseudo regular and pairwise regular are defined and studied in both ech fuzzy soft bi-closure spaces (  bicsp’s) and their induced fuzzy soft bitopological spaces. We also study the relationships between them. We show that in all these types of axioms, the hereditary property is satisfied under closed fs bi-csubsp of . Furthermore, we define some normality axioms, namely pairwise semi-normal, pairwise pseudo normal, pairwise normal and pairwise completely normal in both  bicsp’s and their induced fuzzy soft bitopological spaces, as well as their basic properties and the relationships between them are studied.

(January 25, 2011) represented a real opportunity to bring about fundamental changes in Egyptian foreign policy and to start a new phase that would cut off all the negative and problematic aspects of Egyptian politics in the period before the revolution. Through the employment of Egypt's huge balance and the role of historical is a civilization rooted in the roots of thousands of years and Islamic reference represented over more than a thousand years the Islamic medium of religion in the start of vision and tools to achieve the Egyptian national interest, and safeguarding Egyptian national security in its comprehensive sense. The research attempts to answer a central question: Is there a role for Egyptian soft power in the Islamic world

With the advent of the globalization, the rapid development in technology and the intensity of competition companies attemptto maintain competition advantages and retain customers. The traditional methods in managerial accounting become irrelevance to achieve the objectives of these companies especially with the rapid changes in modern manufacturing environment .Thus there is a need to new tools in accounting such as lean accounting, which is considered as a costing method that support creating value for the customer by costing the entire value stream, eliminating waste in the accounting process, reduced lead time, improved quality, lowered time delivery and increased available capacity. Using value stream focuses not only on the waste&n

ABSRTACT Background: Soft liner material is become important in dental prosthetic treatment. They are applied to the surface of the dentures to achieve more equal force distribution , reduce localized pressure and improve denture retention by engaging undercut . So the aim of the study is to evaluate the effect of different surface treatment by air-abrasion AL2O3 and laser treatment with CO2 laser on improving the shear bond strength of the denture liner to acrylic denture base material . Materials and methods: the 30 specimens of heat cured acrylic denture base material (high Impact acrylic )and heat cured soft liner (Vertex ,Nether Lands )were prepared for this study .They were designed and divided according to type of the s

In this paper, the penetration of the stone column was investigated in order to get the minimum length of the stone column above which the increase in length has little advantage. The effect of using different materials in column are also studied. The material used is granular of different angle of internal friction (). The results of the investigation indicated that the effect of stone column remains constant when the ratio of the thickness of the soft clay layer to the stone column’s diameter is more than 15. The results also indicated that a pronounced effect is obtained when the angle of internal friction of the stone column material is increased.