JORDAN *-DERIVATIONS ON PRIME AND SEMIPRIME *-RINGS

Abstract

Let R be a 2-torsion free *-ring, and d: R→R be a Jordan *-derivation. In this paper
we prove the following results: (1) If R is a non-commutative prime *-ring, and d(h) h +
h d(h)  Z(R) for all h  H(R), then d(h) =0 for all h  H(R).(2) If R be a noncommutative
prime *-ring, and d([x,y])= [x,y] for all x, y  R, then R is normal *-
ring.(3) If R is a semiprime *-ring, then there is no d satisfies d(xy+yx)=xy+yx for all x, y
R, where H(R)={x; x R s.t x*=x }.