Let A and B be two prime -rings. Let : A ! B be a bijective and satisfies (A • P • P) = (A) • (P) • (P), for all A 2 A and P 2 {I, P1, I − P1} where P1 is a projection in A. The operation • between two arbitrary elements S and T in A is defined as S • T = ST +TS for 2 {−1, 1}. Then, if (I) is projection, we show that is additive.
