MMN-1507
Generalized derivations acting as homomorphismor anti-homomorphism with central values in semiprime rings
Abstract
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, y ∈ R. In the present
paper, our main object is to study the situations: (1) F (xy) − F (x)F (y) ∈
Z(R), (2) F (xy) + F (x)F (y) ∈ Z(R), (3) F (xy) − F (y)F (x) ∈ Z(R), (4)
F (xy) + F (y)F (x) ∈ Z(R); for all x, y in some suitable subset of R.
Vol. 16 (2015), No. 2, pp. 781-791
DOI: 10.18514/MMN.2015.1507