group rings which are right gr-ring

A ring r is called a reversible ring, if ab = 0 implies that ba = 0,for every a; b 2 r: many studies have been conducted on reversible grouprings in recent years. the aim of this paper is to generalize some of theprevious results about reversible group rings to more general cases. for thispurpose, we introduce a generalization of reversible rings as right gr-ring,where a right gr-ring is a ring in which ab 2 i implies ba 2 i, for every rightideal i of r and a; b 2 r: we will study conditions under which a group ringr[g] becomes a right gr-ring. we show that the group ring k[q8] of a groupof quaternions q8 over eld k is a right gr-ring if and only if char(k)=0 andthe equation x2 + y2 + 1 = 0 has no solution in k.