Lie Ideals and Centralizing Mappings with Generalized Derivations
Radwan Mohammed Al-Omary *
Department of Mathematics, IBB University, IBB, Yemen.
Nadeem Ur Rehman
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India.
*Author to whom correspondence should be addressed.
Abstract
Let R be a prime ring with char(R) ≠ 2, Z(R) the center of R and L be a nonzero square closed Lie ideal of R. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → Rsuch that F(xy) = xF(y) + d(x)y for all x, y ∈ R. In the present paper we shall show that L ⊆ Z(R) such that Radmitting a generalized derivations F and G associated with derivations d and g respectively, satisfying several conditions.
Keywords: Prime rings, derivations, generalized derivations, lie ideals and centralizing mapping