Rings decomposed into direct sums of J-rings and nil rings - Hisao Tominaga (International Journal of Mathematics and Mathematical Sciences)
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.