The present study introduces the concept of J-pure submodules as a generalization of pure submodules. We  study some of its basic  properties  and  by using this concept we  define the class of  J-regular modules,  where an R-module  M is called  J-regular module if every submodule of M is J-pure submodule. Many results about this concept are proved

In this paper, we introduce and study the notions of fuzzy quotient module, fuzzy (simple, semisimple) module and fuzzy maximal submodule. Also, we give many basic properties about these notions.

      In this work, the notion is defined by using    and some properties of this set are studied also,  and   Ù€ set are two concepts that are defined by using ; many examples have been cited to indicate that the reverse of the propositions and remarks is not achieved. In addition, new application example of nano was studied.

The present study aimed to demonstrate the extent to which the activity of a number of enzymes and genetic variation of β-globin genes were affected in the blood of 65 children with β - thalassemia major of both sexes. The patients, with an age range of 2 – 15 years, were registered in the Thalassemia Center at Ibn Al-Atheer Teaching Hospital for Children in the city of Mosul / Iraq. They were under continuous treatment after being diagnosed by specialist doctors. The study also involved 30 healthy children of both sexes with the same age range who were considered as a control group.

       The results showed significant increases (p≤0.05) in the activities of alanine transaminase (ALT), aspart

     The purpose of this paper is to study a new class of fuzzy covering dimension functions, called fuzzy

      In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule  of an R-module  is called Pr- maximal if  ,for any submodule  of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule  

 of an R-module  is named near (N-maximal) whensoever  is pure submodule of  such that  then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of  is Pr-maximal. A ring  is named Pr-ring if whole proper ideal of  is a Pr-maximal ideal, we offer the concept pure local (Pr-loc

In this paper we define a signal soft set as a mathematical tool to represent and study atoms, anti-atoms, electrons, anti-electrons, protons, and anti-protons, and generate a signal soft topology, with an example of signal soft topology on H₂O.

Around fifty Escherichia coli isolates were isolated from sixty midstream urine specimens collected from patients visiting hospitals in Baghdad city. Approximately, 52% of all isolates were identified as extended spectrum beta lactamases (ESBL) producer. Results demonstrated that 92% of these isolates were sensitive to carbapenems. Only four β-lactamase coding genes were detected; blaTEM, blaPER, blaVIM and blaCTX-M-2. As a conclusion, this work revealed that local E. coli isolates harboured ESBL coding genes which may contribute in its pathogenicity.

The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.