Abstract In this work we introduce the concept of approximately regular ring as generalizations of regular ring, and the sense of a Z- approximately regular module as generalizations of Z- regular module. We give many result about this concept.

High temperature superconductor with nominal composition Bi1.6Pb0.4Sr1.8Ba0.2Ca2 Cu3O10+? was prepared by solid state reaction method. Two sets of samples have been prepared .The first one was quenched in air; the second set was quenched in liquid nitrogen. X-ray diffraction analyses showed an orthorhombic structure with two phases, high –Tc phase (2223) and low-Tc phase (2212) in addition to that impure phase was found. It has been observed that quenched in air samples display a sharp superconducting transition and a higher-Tc phase than that of the quenched in liquid nitrogen samples.

he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga

Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

Background: Malnutrition during human growth affects the size of the tissues at different stages of life, body proportions, body chemistry, as well as quality and texture of tissues. Teeth are particularly sensitive to malnutrition. Malnutrition may affect odontometric measurement involving tooth size dimensions. The aim of this study was to estimate the effect of nutrition on teeth size dimension measurements among students aged 15 years old. Materials and methods: This study was conducted among malnourished group in comparison to well-nourished group matching with age and gender. The present study included 167 students aged 15 years (83 malnourished and 84 well-nourished). The assessment of nutritional status was done by using body mass