Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ A Strongly Nil Clean Rings With Units Of Order Two “

In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics

   Prof. Dr. Duha Bashir Abdullah The esteemed

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Wednesday  21 -8-2024

Master’s thesis by student Samira Beno Toma, under the supervision of  Prof. Dr. Nazar Hamdoon Shuker Mahmood.

If every element of a ring R is the sum of idempotent and nilpotent that commute with one another , then the ring is said to be a strongly nil-clean. Further features of a strongly nil-clean ring are given in this thesis. Furthermore, we present and investigate a special class of  strongly nil-clean rings with order two units. Additionally, we examine a ringwith each element a in R, a^2 and a^4 is a strongly nil-clean with order two and order four units. Among other results, we prove that: If R is a strongly nil-clean ring of order two units, then for all a in R, existing b in R, such that a.b=E,a-b-1=u and u^2=1, and we prove that the converse of this result is also true if 2 is nilpotent..

The thesis concludes with a discussion of the new findings and provides some suggestions for future applications.

The scientific committee included the following members:

• Prof. Husam Qasem Mohammad – Chairman

2- Assist. rof. Dr. Ali Abdulqader alabdali i    – Member.

3- Assist. Prof. Dr. Mohammed Thanoon Younis – Member .

 4- Prof. Dr.Nazar Hamdoon Shuker Mahmood – Member and supervisor.