• SOME RESULTS ON -Lie ideals & GENERALIZED DERIVATIONS

Abstract

Let R be a 2-torsion free -prime ring with involution , U a non zero -Lie ideal and I a nonzero -ideal of R. Let F be a generalized derivation associated with a nonzero derivation d of R commuting with . In the present paper, we discuss the commutativity of a -prime ring R admitting a generalized derivation F satisfying any of the following properties:
(i) d(x) ◦ F(y) = 0, (ii) [d(x), F(y)]= 0, (iii) d(x) ◦ F(y) ± x ◦ y = 0, (iv) [d(x), F(y)] [x, y] = 0 , (v) (d(x) ◦ F(y)) [x, y] = 0,and (vi) [d(x), F(y)] x ◦ y = 0 for all x, y in an appropriate subset of R.

2000 Mathematics subject Classification: 16W10, 16W25, 16U80.

Keywords: Derivations, Lie ideals, rings with involution, σ-prime rings.