Abstract
Let R be a nonassociative ring, N, M and L the left nucleus, middle nucleus and right nucleus respectively. We prove that if R is a semiprime ring and satisfies (R, R, R) ⊆N∩M or M∩L or N∩L the N=M=L and 2(R, R, R)=0. Moreover, if the Abelian subgroup ((R, R, R),+)of(R, +) has no elements of order 2 then R is associative. Thus, E. Kleinfild’s result [1] can be improved.
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