Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.
In this paper ,we introduce a concept of Max– module as follows: M is called a Max- module if ann N R is a maximal ideal of R, for each non– zero submodule N of M; In other words, M is a Max– module iff (0) is a *- submodule, where a proper submodule N of M is called a *- submodule if [ ] : N K R is a maximal ideal of R, for each submodule K contains N properly. In this paper, some properties and characterizations of max– modules and *- submodules are given. Also, various basic results a bout Max– modules are considered. Moreover, some relations between max- modules and other types of modules are considered.
... Show MoreAnew mathematical formula was proposed to describe the behavior of the extinction coefficient as a function of ambient temperature and wavelengths for some of infrared materials. This formula was derived depending on some experimental data of transmittance spectrum versus wavelengths for many ambient temperatures. The extensive study of the spectrum characteristics and depending on Bose-Einstein distribution led to derive an equation connecting the extinction coefficient or the absorption coefficient with the ambient temperature and wavelengths of the incident rays. The basic assumption in deriving process is the decreasing in transmittance value with the increasing temperature which is only due to the changing in extinction coeffi
... Show MoreWe present the concept of maps Γ- periodi2 on Γ -near-ring S. Our main goal is to research and explore the presence and mapping traits such as h Γ –hom anti-Γ –hom, Γ –α-derivations of Γ -periodi2 on Γ- near-rings.
The present paper concerns with the problem of estimating the reliability system in the stress – strength model under the consideration non identical and independent of stress and strength and follows Lomax Distribution. Various shrinkage estimation methods were employed in this context depend on Maximum likelihood, Moment Method and shrinkage weight factors based on Monte Carlo Simulation. Comparisons among the suggested estimation methods have been made using the mean absolute percentage error criteria depend on MATLAB program.
An R-module M is called a 2-regular module if every submodule N of M is 2-pure submodule, where a submodule N of M is 2-pure in M if for every ideal I of R, I2MN = I2N, [1]. This paper is a continuation of [1]. We give some conditions to characterize this class of modules, also many relationships with other related concepts are introduced.
The effects of Internet use on university’s students:The effects of Internet use on university’s students:“A Study on a Sample of Jordanian University’s students "This survey aims to identify the most important effects of Internet use on Jordanian public and private universities’ students by monitoring and analyzing a set of indicators that show the quality of the effects on specific fields such as cultural, social, psychological, moral and political effects .To achieve these goals, the study attempts to answer the following questions:1. What are the effects of Internet’s use on students?2. What is the relationship between the effects and demographic variables such as gender, age, family size an
... Show MoreBackground: The beneficial gut bacterium E. coli can cause blood poisoning, diarrhoea, and other gastrointestinal and systemic disorders. Objective: This study amid to examines the antibiofilm activity of Laurus nobilis leaves extract on E. coli isolates and compares pre- and post-treatment gene expression of fimA and papC genes. Subjects and Methods: Ten isolates of E. coli were obtained from the Genetic Engineering and Biotechnology Institute, University of Baghdad, which was previously collected from Baghdad city hospitals and diagnosed by chemical tests, the diagnosis was confirmed using VITEK-2 System. The preparation of the aqueous and methanolic Laurus nobilis leaves extracts was done by using the maceration method and Soxhlet appara
... Show MoreThe aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz
... Show MoreA disagreement has arisen among scholars regarding the ruling on historical statues and monuments in Muslim countries, especially after the Taliban blew up some huge historical statues, and we have witnessed different positions that reach the point of contradiction, each claiming to be right, and now that the crisis has passed and the intensity of the dispute has subsided, I see It is appropriate to discuss this issue calmly, without drifting behind this or that party, to find out the legal position on these statues and monuments.
I presented the most prominent modern opinions related to the subject and discussed them in this research, which I called (Sharia’s position on historical statues and monuments), in which I tried to reach