The main goal of this paper is to give  a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of  purely hollow modules is considered.

A submodule Ϝ of an R-module Ε is called small in Ε if whenever  , for some submodule W of Ε , implies  . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if  , such that  , then  , where  is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .

Urban morphological approach (concepts and practices) plays a significant role in forming our cities not only in terms of theoretical perspective but also in how to practice and experience the urban form structures over time. Urban morphology has been focused on studying the processes of formation and transformation of urban form based on its historical development. The main purpose of this study is to explore and describe the existing literature of this approach and thus aiming to summarize the most important studies that put into understanding the city form. In this regard, there were three schools of urban morphological studies, namely: the British, the Italian, and the French School. A reflective comparison between t

HS Saeed, SS Abdul-Jabbar, SG Mohammed, EA Abed, HS Ibrahem, Solid State Technology, 2020

One of the scientific education aims, preparing a student able to keep up with the scientific developments and innovations around him and make him contribute, adapt, investment and continue development. The concepts of nanotechnology from scientific innovation open up an important area of thinking and intervention in the field of chemistry applications in daily life, the technological changes lead to social, political and economic changes which result that the students to have the knowledge, understanding, awareness, appreciation and sense in applications of modern technology for their use optimally, in order to cope with these scientific and technological changes. The research aims at finding out the correlation between the acquisi

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.

     Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between prime submodules of a given module and the extension of prime submodules. The relations between prime submodules of two given modules and the prime submodules in the direct product of their quotient module are studied and investigated.