Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.

The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

In this paper, we present the almost approximately nearly quasi compactly packed (submodules) modules as an application of the almost approximately nearly quasiprime submodule. We give some examples, remarks, and properties of this concept. Also, as the strong form of this concept, we introduce the strongly, almost approximately nearly quasi compactly packed (submodules) modules. Moreover, we present the definitions of almost approximately nearly quasiprime radical submodules and almost approximately nearly quasiprime radical submodules and give some basic properties of these concepts that will be needed in section four of this research. We study these two concepts extensively.

        A new generalizations of coretractable modules are introduced where a module  is called t-essentially (weakly t-essentially) coretractable if for all proper submodule  of , there exists f End( ), f( )=0 and Imf _tes  (Im f + _tes ). Some basic properties are studied and many relationships between these classes and other related one are presented.

        Let R be a commutative ring with  identity . In this paper  we study  the concepts of  essentially quasi-invertible submodules and essentially  quasi-Dedekind modules  as  a generalization of  quasi-invertible submodules and quasi-Dedekind  modules  . Among the results that we obtain is the following : M  is an essentially  quasi-Dedekind  module if and only if M is aK-nonsingular module,where a module M is K-nonsingular if, for each  , Kerf ≤_e M   implies   f = 0 .

 Abstract

In order to determine what type of photovoltaic solar module could best be used in a thermoelectric photovoltaic power generation. Changing in powers due to higher temperatures (25^oC, 35^oC, and 45^oC) have been done for three types of solar modules: monocrystalline , polycrystalline, and copper indium gallium (di) selenide (CIGS). The Prova 200 solar panel analyzer is used for the professional testing of three solar modules at different ambient temperatures; 25^oC, 35^oC, and 45^oC and solar radiation range 100-1000 W/m². Copper indium gallium (di) selenide module   has the lowest power drop (with the average percent