International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 205-207
Rings decomposed into direct sums of -rings and nil rings
Department of Mathematics, Okayama University, Okayama 700, Japan
Received 25 April 1984
Copyright © 1985 Hisao Tominaga. 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 (not necessarily with identity) and let denote the set of idempotents of . We prove that is a direct sum of a -ring (every element is a power of itself) and a nil ring if and only if is strongly -regular and is contained in some -ideal of . As a direct consequence of this result, the main theorem of  follows.