equivalent conditions for the notion of right gr-ring

Reversible rings have been extensively studied in recent years. in [6], we tried to obtain some of the results obtained so far about reversible rings under better conditions. for this purpose, we introduced the notion of right gr-ring as a class of reversible rings, in [6]. in this paper, we investigate equivalent conditions for the definition of right gr-ring in domains,rings with zero jacobson radical, von neumann, semisimple and right primitive rings. we prove that a semisimple ring r is a right gr-ring iff r is a finite direct product of division rings. also, we will show that a von neumann ring r is a right gr-ring iff r is a reduced ring.