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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 Hindawi Publishing Corporation. 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 x and y, there exist positive integers k,l,m, and n with either km or ln, 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.