Let R be an individual left R-module of the same type as W, with W being a ring containing one. W’s submodules N and K should be referred to as N and K, respectively that K ⊆ N ⊆ W if N/K <<_J (D_j (W)+K)/K, Then K is known as the D J-coessential submodule of Nin W as K⊆_ (Rce) N. Coessential submodule is a generalization of this idea. These submodules have certain interesting qualities, such that if a certain condition is met, the homomorphic image of D J- N has a coessential submodule called D J-coessential submodule.

In this ˑwork, we present theˑ notion of the ˑgraph for a KU-semigroup as theˑundirected simple graphˑ with the vertices are the elementsˑ of and weˑˑstudy the ˑgraph ofˑ equivalence classesˑofˑ which is determinedˑ by theˑ definition equivalenceˑ relation ofˑ these verticesˑ, andˑ then some related ˑproperties areˑ given. Several examples are presented and some theorems are proved. Byˑ usingˑ the definitionˑ ofˑ isomorphicˑ graph, ˑwe showˑ thatˑ the graphˑ of equivalence ˑclasses ˑand the ˑgraphˑof ˑa KU-semigroup ˑ areˑ theˑ sameˑ, in special cases.

      In this Ë‘work, we present theË‘ notion of the Ë‘graph for a KU-semigroup  as theË‘undirected simple graphË‘ with the vertices are the elementsË‘ of  and weË‘Ë‘study the Ë‘graph ofË‘ equivalence classesË‘ofË‘  which is determinedË‘ by theË‘ definition equivalenceË‘ relation ofË‘ these verticesË‘, andË‘ then some related Ë‘properties areË‘ given. Several examples are presented and some theorems are proved. ByË‘ usingË‘ the definitionË‘ ofË‘ isomorphicË‘ graph, Ë‘we showË‘ thatË‘ the graphË‘ of equivalence Ë‘classes Ë‘and the Ë‘graphË‘of Ë‘a KU-semigroup Ë‘  areË‘ theË‘ sameË‘,

           Let R be  commutative Ring , and let T be  unitary left .In this paper ,WAPP-quasi prime submodules are introduced as  new generalization of Weakly quasi prime submodules , where  proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR , t ϵT, implies that either  r tϵ C +soc   or  s tϵC +soc  .Many examples of characterizations and basic properties are given . Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are established.

Background: The marginal adaptation has a key role in the success and longevity of the fixed dental restoration, which is affected by the impression and the fabrication techniques .The objective of this in vitro study was to evaluate and compare the marginal fitness of lithium disilicate crowns using two different digital impression techniques (direct and indirect techniques) and two different fabrication techniques (CAD/CAM and Press techniques). Materials and Methods: Thirty two sound upper first premolar teeth of comparable size extracted for orthodontic reason were selected in this study .Standardized preparation of all teeth samples were carried out with modified dental surveyor to receive all ceramic crown restoration with 1 mm deep

The current research aims to reveal the level of satisfaction of the mentors with the evaluation of their performance according to gender (male - female) and to formulate the predictive equation for the level of performance (dependent variable) from knowing the level of satisfaction with the evaluation (independent variable). (16 paragraphs) contains alternatives to the answer that measures the level of satisfaction (weak, medium, and high) (1,2,3), that is, with a hypothetical average of (32). It consisted of 100 educational counselors consisting of 45 males and 55 females, the results of the research concluded that the level of satisfaction with performance is below the mean when compared with the hypothetical average of the scale of s

this research is to identify the level of information awareness of the chemistry students in their fourth year studying at Ibn Al-Haytham Education College of pure sciences at the University of Baghdad. The research sample consisted of (107) male and female students out of the total number of (153) students studying during the (2017-2018) academic year, The sample therefore represents 71% of the total students. The research methodology used consisted of two parts. The first part is concerned with measuring information awareness using a multiple choice type of test related to (40) issues. The students were required to select the between (5) alternative answers for each issue. The objectives of the test and the issues used are to measure the

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Abstract Study aim: to assess the influence of care burden for children with leukemia on their mothers` psychosocial status. Methodology: A Descriptive study, conducted at two pediatric hospitals in Baghdad city. A purposive sample of (60) mothers was participated in the study after obtaining their consent form. The instrument of the study was used to assess mothers` psychosocial status in addition to their sociodemographic characteristics. The data was processed and statistically analysed by SPSS program version 23. Result: the result of the study showed mothers have (81%) in self esteem, (77%) in psychosocial distress, (80%) for social interaction, and (76%) for social isolation. There were association between mothers` psychosocial status