International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 205-207
doi:10.1155/S0161171285000230

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

Abstract

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.