MULTIPLICATIVE GENERALIZED DERIVATIONS ON LIE IDEALS IN SEMIPRIME RINGS II

Abstract

Let R be a semiprime ring and L is a Lie ideal of R such that L 6 not subset of Z(R) A map F : R -> R is called a multiplicative generalized derivation if there exists a map d : R -> R such that F(xy) = F(x)y + x d(y), for all x, y is an element of R . In the present paper, we shall prove that d is a commuting map on L if any one of the following holds: i) F(uv) = +/- uv, ii) F(u v) = +/- vu, iii) F(u) F(v) = -/+ uv, iv) F(u) F(v) = +/- vu, v) F(u) F(v) +/- uv is an element of Z, vi) F(u) F(v) +/- vu is an element of Z, vii) [F(u), v] +/- [u, G(v)] = 0; for all u, v is an element of L