Master’s Thesis by “Hadeel khalid Mohammed Qasim” Department of Mathematics

Discussion of the Master’s Thesis Submitted to the College of Computer Science and Mathematics, Department of Mathematics, Entitled:

“On TT-nil clean rings”

supervised by  Prof. Dr. Nazar Hamdoon shuker

In this thesis, we introduce the notion of  TT-nil clean rings (TTNC-ring for short). A  NC-ring is a ring in which for every  in     or   where  is a tripotent    is nilpotent and   The fundamental structural properties of these rings are investigated in detail. Furthermore,  the relationships between TT-nil clean rings and  other known types of rings in the theory such as strongly 2-nil clean and  weakly nil clean rings are examined. We also show the structure of  these rings, and study the structure of the Jacobson radical and right singular ideal in these rings. In addition we introduce the concept of an invo TT clean ring  which is a ring with every  in    or    where  is a tripotent and  is a unit of order two.  Some basic properties of such rings, and their relation with other related rings are investigated.

     The discussion committee consists of

• Hussam Qasim Mohammed (Chairman)
• Shaimaa Hatem Ahmed (Member)
• Ikram Abdul qadir Saleh (Member)
• Nazar Hamdoon shuker (Member and Supervisor)