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LetRbe a ring (not necessarily with identity) and letEdenote the set of idempotents ofR. We prove thatRis a direct sum of aJ-ring (every element is a power of itself) and a nil ring if and only ifRis stronglyπ-regular andEis contained in someJ-ideal ofR. As a direct consequence of this result, the main theorem of  follows.doi:10.1155/s0161171285000230 fatcat:mq4tefpporfglg4q5lwghapkvi