Some results on left (?, ? )?Jordan ideals and one sided generalized derivations

Abstract

Let R be a prime ring with characteristic not 2 and ?, ?, ?, ?, ?, µ, ? automorphisms of R. Let h : R ?? R be a nonzero left (resp. right)- generalized (?, ?)? derivation associated with (?, ?)? derivation d1 (resp. d). Let W, V be nonzero left (?, ? )?Jordan ideals of R and I a nonzero ideal of R. In this paper we also study the situations. (1) ah(R)b ? C?,µ(R) (2) bh(I, a)?,? = 0 or h(I, a)?,? b = 0, (3) bh(I) ? C?,µ(W) or h(I)b ? C?,µ(W), (4) h(I) ? C?,µ(J), (5) (h(R), a)?,? ? C?,?(R), (6) (h(I)b, a)?,µ = 0, (7) b?(W) ? C?,µ(V ) or ?(W)b ? C?,µ(V ).