Let R be an associative ring with identity and let M be a unitary left R–module. As a generalization of small submodule , we introduce Jacobson–small submodule (briefly J–small submodule ) . We state the main properties of J–small submodules and supplying examples and remarks for this concept . Several properties of these submodules are given . Also we introduce Jacobson–hollow modules ( briefly J–hollow ) . We give a characterization of J–hollow modules and gives conditions under which the direct sum of J–hollow modules is J–hollow . We define J–supplemented modules and some types of modules that are related to J–supplemented modules and int

The purpose of this paper is to prove the following result : Let R be a 2-torsion free prime *-ring , U a square closed *-Lie ideal, and let T: RR be an additive mapping. Suppose that 3T(xyx) = T(x) y*x* + x*T(y)x* + x*y*T(x) and x*T(xy+yx)x* = x*T(y)x*2 + x*2T(y)x* holds for all pairs x, y  U , and T(u) U, for all uU, then T is a reverse *-centralizer.

The current research aims to identify: 1. The level of mathematical construct among the Department of Mathematics students in the colleges of education and basic education. 2. The level of effective mathematical operations in both sides of the brain at the Department of Mathematics students in the colleges of education and basic education. 3. The strength and direction of the correlation between the mathematical construct and effective mathematical operations on both sides of the brain at the Department of Mathematics students in the colleges of Education and Basic Education. To investigate the research objectives, the researcher formulated zero-main hypothesis for each aim and from the same hypothesis, three sub-zero hypotheses are deri

Denture cleansing is an essential step that can stop cross‑contamination and adds to the health of the patient, denture durability, and the general quality of life. A disinfection technique must be practical and devoid of damaging effects on the material's properties used to construct the denture base. The main aim of this study is to evaluate the effect of three concentrations of electrolyzed water denture cleanser on heat cure acrylic and polyamide after immersion in electrolyzed water. The evaluation is based on their efficacy on surface hardness, wettability, and color stability compared with one submerged in distilled water as a control group. The method consists of eighty samples of heat-cured acrylic and polyamide material.

Background: Periodontitis is a long-standing infection that destroys the gums, periodontal ligaments, and the alveolar bone that supports the teeth. Inflammation of the gums and chronic periodontitis are both caused by the bacteria in the dental plaque and the herpes viruses, especially types 1 and 2 of the herpes simplex virus.

Objectives: To compare the ELISA and real-time PCR as ways to detect the herpes simplex virus in breast cancer pat

Background: It is still difficult to give a final diagnosis in chronic myeloproliferative disorders (CMPDs) because of the overlap of the common pathological and clinical features of these disorders like bone marrow fibrosis which is considered important because it affects the normal function of the bone marrow. The collagen fibers are of different types, but in the bone marrow, the two main types are: collagen I, which is the most abundant type and collagen III (reticular) which is often associated with type I.
Objectives:To study bone marrow fibrosis (BMF) in samples of bone marrow biopsies (BMB) of chronic myeloid leukemia (CML) and other chronic myeloproliferative disorders using histochemical stains to establish the grade of fibr