International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 531-534
Direct sums of -rings and radical rings
Department of Mathematics, Claina University of Mining and Technology, Jiangsu, Xuzhou 221008, China
Received 4 October 1993; Revised 20 May 1994
Copyright © 1995 Xiuzhan Guo. 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.
Let be a ring, the Jacobson radical of and the set of potent
elements of . We prove that if satisfies given , in there exist integers
and such that and if each is
the sum of a potent element and a nilpotent element, then and are ideals and . We also prove that if satisfies and if each has a representation
in the form , where and ,then is an ideal and .