Right (?,?) —lie 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, a, b ? R. and U, V nonzero right (?, ? )?Lie ideals of R. The main object in this article is to study the situations. (1) a[U, b]?,µ = 0 or [U, b]?,µa = 0, (2) a(U, b)?,µ = 0 or (U, b)?,µa = 0, (3) bh(I) ? C?,µ(U) or h(I)b ? C?,µ(U), (4) (b, U)?,µ = 0 or [b, U]?,µ = 0, (5) (U, b)?,µ ? C?,µ(R), (6) bV ? C?,µ(U) or V b ? C?,µ(U). Also, some characteristics of left and right generalized (?, ?)?derivation satisfying several conditions on ideals are given.