International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 6, Pages 417-420
doi:10.1155/S0161171201001181
On periodic rings
Xiankun Du1
and Qi Yi2
1Department of Mathematics, Jilin University, Changchun 130012, China
2Jilin Commercial College, Changchun 130062, China
Abstract
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.