24 July، 2025
Master’s thesis by Student Rana Mohammed Shafik yahya
Discussion of the master’s thesis in the College of Computer Science and Mathematics -Department of
Mathematics Sciences entitled:
“ The Strongly Tri-nil Clean Rings“
It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Wednesday, -3-2025.
Master’s thesis by Student Rana Mohammed Shafik yahya
under the supervision of Prof. Dr. Nazar Hamdoon Shuker
In this thesis, we consider two closely related classes of rings that generalize the concept of nil clean rings. We consider strongly tri-nil clean rings(STNC), i.e., rings where every element can be written as a sum of a tripotent element (an element such that ) and a nilpotent element, which commute. We give some fundamental properties and structure theorems of STNC rings, including criteria under which an STNC ring is strongly nil-clean and characterizations linking STNC rings with tripotent rings. In addition, we establish the notion of STNC rings with involution units, We provide examples of this class and prove that all such STNC rings with involution units are strongly invo clean. We also prove that the Jacobson radical is a nil ideal in these rings and that they satisfy Zhou’s conditions for nil-clean rings.
The scientific committee included the following members:
- Dr. Husam Qasem Mohammad – Chairman
- Dr. Ali Abdalkader Belal Alabdly – Member.
- Prof. Dr. Zubaida Muhammed Ibrahem – Member.
- Dr. Nazar Hamdoon Shuker – Member and supervisor.
