International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 6, Pages 417-420
On periodic rings
1Department of Mathematics, Jilin University, Changchun 130012, China
2Jilin Commercial College, Changchun 130062, China
Received 23 April 1997; Revised 31 October 1997
Copyright © 2001 Xiankun Du and Qi Yi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is proved that a ring is periodic if and only if, for any
elements and , there exist positive integers , and with either or , depending on and , for which . Necessary and sufficient conditions are
established for a ring to be a direct sum of a nil ring and a -ring.