GENERALIZED DERIVATIONS ACTING AS HOMOMORPHISM OR ANTI-HOMOMORPHISM WITH CENTRAL VALUES IN SEMIPRIME RINGS.

Let R be a semiprime ring with center Z(R). A mapping F: R→ R is called a generalized derivation if there exists a derivation d : R→R such that F(xy) = F(x)y+xd(y) holds for all x,yϵR. In the present paper, our main object is to study the situations: (1) F(xy)-F(x)F (y)ϵ Z(R), (2) F(xy)+F(x)F(y)ϵ Z(R), (3) F(xy)-F(y)F(x) ϵ Z(R), (4) F(xy)+F(y)F(x) ϵ Z(R); for all x,y in some suitable subset of R. [ABSTRACT FROM AUTHOR]