25 August، 2025
Master’s thesis by Student Mohammed Ismael Jumaah Salman
Discussion of the master’s thesis in the College of Computer Science and Mathematics -Department of
Mathematics Sciences entitled:
“ The Four Potent Nil Clean Rings“
It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Monday,25 -8-2025.
Master’s thesis by Student Mohammed Ismael Jumaah Salman
under the supervision of Prof. Dr. Nazar Hamdoon Shuker
A ring is said to be four potent if every element satisfies the identity. for every . This thesis begins by establishing the fundamental properties of four potent rings. It then introduces the concept of a generalized four potent ring, in which each element satisfies , meaning that the square of each element is four potent. The core structural properties of such rings are studied in detail. The relationships between generalized four potent rings and other algebraic structures, such as strongly 2-nil clean rings, are examined. Furthermore, the thesis introduces and investigates generalized four potent nil clean rings, focusing on their defining characteristics. Special emphasis is placed on the role of the Jacobson radical and the right singular ideal within these rings. All results are supported by rigorous proofs, and illustrative examples are provided to clarify the theoretical findings.
The scientific committee included the following members:
- Dr. Husam Qasem Mohammad – Chairman
- Prof. Dr. Bedaa Suhel Abdulla – Member.
- Prof. Dr. Zubaida Muhammed Ibrahem – Member.
- Dr. Nazar Hamdoon Shuker – Member and supervisor.
