In this work, we introduced the Jacobson radical (shortly Rad (Ș)) of the endomorphism semiring Ș =  ( ), provided that  is principal P.Q.- injective semimodule and some related concepts, we studied some properties and added conditions that we needed. The most prominent result is obtained in section three

-If   is a principal self-generator semimodule, then (_ȘȘ) = W(Ș).

Subject Classification: 16y60

This study aims to develop a recommendation engine methodology to enhance the model’s effectiveness and efficiency. The proposed model is commonly used to assign or propose a limited number of developers with the required skills and expertise to address and resolve a bug report. Managing collections within bug repositories is the responsibility of software engineers in addressing specific defects. Identifying the optimal allocation of personnel to activities is challenging when dealing with software defects, which necessitates a substantial workforce of developers. Analyzing new scientific methodologies to enhance comprehension of the results is the purpose of this analysis. Additionally, developer priorities were discussed, especially th

This research aims to identify the impact of Daniel's model on the development of critical thinking. In order to achieve this objective, the following hypotheses are formulated: 1. There is no statistically significant difference at the significance level (0.05) between the average differences in the posttest scores of the experimental group taught according to Daniel's model and the control group taught according to the traditional method in the measure of critical thinking. 2. There is no statistically significant difference at the significance level (0.05) between the average differences in the preand post-tests scores of the experimental group taught according to Daniel's model in the measure of critical thinking. The current research i

Heritage reflects peoples' memory and essence of nations. Thus, this divan was really the material and tool for writers in general and poets in specific both in their artificial innovations . Accordingly, modern writers have endeavored to bring heritage back in all its details and occurrences. Abdullwahab Al-Bayati's experience had reflected his innovative and strong link with the humanitarian heritage, in that heritage in view of Al-Bayati means both the humanitarian expertise and gains that are able to extend from past to future passing through the present.From this, the poet had not disconnected his strong link with the Arab poetic heritage .Thus, the poet had utilized the Arab poetic heritage in expressing on the Arab contrary realit

Background: Fractures of the humeral shaft
accounting for approximately 3% of all
fractures. There is a wide array of good
options for their treatment and controversy
over the best methods. Although good
techniques of osteosynthesis are available, the
aim of this article is toemphasize on the benefit
and good outcome of conservative treatment
for properly selected cases to decrease the cost
and avoid the complications of surgery.

Low bearing capacity of weak soil under shallow footings represents one of construction problems.
Kaolin with water content converges to liquid limit used to represent the weak soil under shallow
footing prototype. On the other hand, fly ash, which can be defined as undesirable industrial waste
material, was used to improve the bearing capacity of the soft soil considered in this research. The soft
soil was prepared in steel box (36×36×25) cm and shallow square footing prototype (6×6) cm were
used .Group of physical and chemical tests were conducted on kaolin and fly ash. The soft soil was
improved by a bed of compacted fly ash placed under the footing with dimensions equal to that of
footing but with different de

Receipt date:3/13/2021 accepted date:5/26/2021 Publication date:12/31/2021

 This work is licensed under a Creative Commons Attribution 4.0 International License.

energy is one of the strategic resources within international politics, and this is through the existing competition between the international powers on it, and the global powers have begun to rely on interest in new areas, such as import, depending on new projects an

Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of Messengers, Muhammad and his family

The good and pure and after his companions

God Almighty said: ( ) Do they not contemplate the Qur’an? If it had been from other than God, they would have found in it much discrepancy. God Almighty has made the well-being of people and their lives linked to faith in it. So what is the need of people today to return to the Book of their Lord so that they may return to the right path that God intended for His servants so that they may attain sustenance? Security and the good life. How could it not be, when many of the nations of the world no longer see security or stability because their leaders and politic

The Research deals with the negative phenomena which appeared in the urban scenes of the  Iraqi cities after 2003, particularly trespassing the architectural design of the urban Individual houses.  Many academic researchers , critics, and cultural circles, drawn attention to the impact of  political and cultural variable change on such phenomena  without detailed  analysis . The research problem  is set according to central questions : If the phenomena is the trespass , what
are the sides which are being trespassed  in the division of the individual house? , If the diagnosis of the phenomena denotes perceived repetition of the cases , So what's size of this transposes on the architectural design of t

Diyala river is the most important tributaries in Iraq, this river suffering from pollution, therefore, this research aimed to predict organic pollutants that represented by biological oxygen demand BOD, and inorganic pollutants that represented by total dissolved solids TDS for Diyala river in Iraq, the data used in this research were collected for the period from 2011-2016 for the last station in the river known as D17, before the river meeting Tigris river in Baghdad city. Analysis Neural Network ANN was used in order to find the mathematical models, the parameters used to predict BOD were seven parameters EC, Alk, Cl, K, TH, NO3, DO, after removing the less importance parameters. While the parameters that used to predict TDS were fourte