International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 205-207

Rings decomposed into direct sums of J-rings and nil rings

Hisao Tominaga

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 R be a ring (not necessarily with identity) and let E denote the set of idempotents of R. We prove that R is a direct sum of a J-ring (every element is a power of itself) and a nil ring if and only if R is strongly π-regular and E is contained in some J-ideal of R. As a direct consequence of this result, the main theorem of [1] follows.