College of Computer Science and Mathematics

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

“ Locally Involution Regular Rings “

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday, 28 -7-2025.

Master’s thesis   by Student Yasmine Mohammed Ismail

under the supervision of  Ass.Prof.Zubaida Mohammed Ibraheem Ismail

A ring R is called locally right (left) semi involution regular ring , if for every  , either  or  is right (left) semi involution regular element .

In this work we study some new properties of locally right semi involution regular rings and the relations between this rings and locally involution regular rings , involution regular rings and clean rings . The main results that were obtained:

• Let be a ring . Then is L.r.s.I.Reg. iff , or    is  direct summand for all  , where    for some
• Every associate elements in is idempotent , if ). where p is prime number and
• Let R be L.I.Reg. ring and I is an proper ideal  of R , Then   is L.r.s.I.Reg.Ring .
• Let be abelian L.r.s.I.Reg.Ring , then every element can be written as  or  where is right semi invo- regular and  is nilpotent element.
• Every L.I.Reg.Ring is L.r.s.I.Reg.Ring.

Let R be a L.r.s.I.Reg.Ring and  is P-injective , then R is L.I.Reg.Ring , when        for all  ,  .

The scientific committee included the following members:

• Dr. Laith Abdullatif Majeed – Chairman
• Dr. Raida Dawood Mahmood- Member.
• Dr. Ammar Sadiq Mahmood – Member.
• Prof. Zubaida Mohammed Ibraheem- Member and supervisor.