MMN-689
On Lie ideals and generalized derivations of *-prime rings
Shuliang Huang; Öznur Gölbaşi;Abstract
Let .R; / be a 2-torsion free -prime ring with involution and center Z.R/, U a
nonzero square closed -Lie ideal of R. An additive mapping F W R ! R is called a generalized
derivation if there exits a derivation d W R ! R such that F .xy/ D F .x/y Cxd.y/. In the present
paper, we prove that U Â Z.R/ if any one of following conditions holds: 1) ŒF .u/; u D 0;
2) Œd.u/; F .v/ D 0; 3) d.u/oF .v/ D 0; 4) Œd.u/; F .v/ D ̇Œu; v; 5) d.u/oF .v/ D ̇uov; 6)
d.u/F .v/ ̇ uv 2 Z.R/; for all u; v 2 U: Furthermore, an example is given to demonstrate that
the -primeness hypothesis is not superfluous.
Vol. 14 (2013), No. 3, pp. 941-950
DOI: 10.18514/MMN.2013.689