MULTIPLICATIVE GENERALIZED DERIVATIONS ON LIE IDEALS IN SEMIPRIME RINGS II.

Let R be a semiprime ring and L is a Lie ideal of R such that L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+xd(y), for all x,y∈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(uv)=±vu, iii) F(u)F(v)=±uv, iv) F(u)F(v)=±vu, v) F(u)F(v)±uv∈Z, vi) F(u)F(v)±vu∈Z, vii) [F(u),v]±[u,G(v)]=0, for all u,v∈L. [ABSTRACT FROM AUTHOR]