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 group rings in recent years. The aim of this paper is to generalize some of the previous results about reversible group rings to more general cases. For this purpose, 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 right ideal I of R and a; b 2 R: We will study conditions under which a group ring R[G] becomes a right gr-ring. We show that the group ring K[Q8] of a group of quaternions Q8 over eld K is a right gr-ring if and only if char(K)=0 and the equation x2 + y2 + 1 = 0 has no solution in K.