REMARKS ON GENERALIZED DERIVATIONS IN ∗−PRIME RINGS

Let (R, ∗) be a ∗−prime ring with characteristic different from two, and L ̸= ۰be a square closed ∗−Lie ideal of R. An additive mapping F : R −→ R is calleda generalized derivation on R if there exists a derivation d : R −→ R such thatF(xy) = F(x)y + xd(y) for all x, y ∈ R. In the present paper, we shall show thatwhen L satisfies any of several identities in F, then L is central.

کلیدواژه ها:

∗-Lie ideals ، involution ، ∗-prime rings ، derivations and generalized derivations