in this thesis, the cleanness of regular elements in quasi-morphic rings having internal-cancelltion has been derived. We show that if is a quasi-morphic ring and has internal-cancelltion, and let e regular, then is the sum of an idempotent and an invertible element. It is further proved that condition that is regular and is regular in above theorem are not necessary. We also investigate as to when regular elements in a morphic or quasi-morphic ring can be expressed as the sum of two units.
