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.

    The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then Ais called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

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 definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then A is called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

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

This research included isolation of 18 bacterial isolates from children stool with diarrhea and acute bloody water and under the age of five, if possible get a 9 isolates of the bacterium Escherichia coli and 5 isolates of the bacterium Salmonella typhimurium and 4 isolation of the bacterium Shigella flexneri, subjected all of these isolates tests AGRO and microscopic and biochemical and diagnosed using Vitek2 system. Tested the effectiveness of inhibitory extract alcohol to peel pomegranate Punica granatum L. in the growth of isolates bacterial intestinal and using the diffusion method in drilling Well diffusion as well as determine the focus damper Near Minimum inhibitory concentration MIC and focus killer Near Minimal bactericidal con

In vitro tests have been carried out to find out the efficacy of watery extracts of garlic Allium sativum and hot pepper Capsicum spp. against the trophozoites of Entamoeba histolytica cultivated in liver infusion agar media at 37 c . The doses of ( 0.01, 0.05 ,0.1, 0.5, 1 ml )of garlic and hot pepper watery extracts were added to certain number of E. histolotica trophozoits for exposure time of 24 hrs., the mortality percentage of trophozoites treated with garlic extract were ( 14.82 %, 31.05% ,46.16% , 64.29% , 92.7%) respectively , these percentages were very close to that obtained from the treatment with the hot peper extract which were (17.86%, 32% , 44% ,66.67% ,100%) respectively . Generally these results showed that the ga

Background: Dental erosion is a common oral condition which results due to consumption of high caloric and low pH acidic food such as carbonated drinks and fruit juices. It is expected that these food types can cause irreversible damage to dental hard tissues and early deterioration of the dental restorations. So, this study aimed to evaluate and compare the erosive potential effects of orange fruit juice and Miranda orange drink on the microhardness of an orthodontic composite material. Materials and methods: Thirty discs with a thickness of 2 mm and a diameter of 10 mm were prepared from orthodontic bonding composite. The prepared discs were equally divided into three groups (n=10). Microhardness analysis was carried out both prior to