On periodic rings - Xiankun Du; Qi Yi (International Journal of Mathematics and Mathematical Sciences)
It is proved that a ring is periodic if and only if, for any elements x and y, there exist positive integers k,l,m, and n with either k≠m or l≠n, depending on x and y, for which xkyl=xmyn. Necessary and sufficient conditions are established for a ring to be a direct sum of a nil ring and a J-ring.