Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.

Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.

 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

Let R be a commutative ring with unity 1 6= 0, and let M be a unitary left module over R. In this paper we introduce the notion of epiform∗ modules. Various properties of this class of modules are given and some relationships between these modules and other related modules are introduced.

   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.

      In this paper, we introduced module that satisfying strongly -condition modules and strongly -type modules as generalizations of t-extending. A module  is said strongly -condition if for every submodule of  has a complement which is fully invariant direct summand. A module   is said to be strongly -type modules if every t-closed submodule has a complement which is a fully invariant direct summand. Many characterizations for modules with strongly -condition for strongly -type module are given. Also many connections between these types of module and some related types of modules are investigated.

The high temperature superconductor’s compounds are one of the hot spot field of science, due to their applications in industries. Hg0.8Sb0.2Ba2Ca2Cu3O8+δ and Hg0.8Sb0.2Ba2Ca1Cu2O6+δ, were manufactured using a doable-step of solid state reaction method. The samples were sintered at 800 ° C. The transition temperatures Tc are found from electrically resistively by using four probe techniques. The resistivity become zero when the transition temperature Tc(offset) have 131 and 119 K, and the onset temperature Tc(onset) have 139 K for Hg0.8Sb0.2Ba2Ca2Cu3O8+δ and 132 K for Hg0.8Sb0.2Ba2Ca1Cu2O6+δ. Analysis of X-ray diffraction showed a tetragonal structure with lattice parameters changes for all samples.

The aim of this paper is to construct cyclic subgroups of the projective general linear group over  from the companion matrix, and then form caps of various degrees in . Geometric properties of these caps as secant distributions and index distributions are given and determined if they are complete. Also, partitioned of  into disjoint lines is discussed.

The main aim of this paper is to introduce the relationship between the topic of coding theory and the projective plane of order three. The maximum value of size of code over finite field of order three and an incidence matrix with the parameters,  (length of code),  (minimum distance of code) and  (error-correcting of code ) have been constructed. Some examples and theorems have been given.