On Centralizing and Generalized Derivations Of prime Rings with involution

Radwan Mohammed Al-omary; Nadeem Ur Rehman

Radwan Mohammed Al-omary Department of Mathematics IBB University IBB, YEMEN http://orcid.org/0000-0001-5334-6169
Nadeem Ur Rehman Department of Mathematics, Aligarh Muslim University Aligarh 202002, India

Keywords: Lie ideals, prime rings, centralizing, derivations and generalized derivations

Abstract

Let (R,∗) be a 2-torsion free ∗-prime ring with involution ∗, L= 0 be a nonzero square closed ∗-Lie ideal of R and Z the center of R. An additive mapping F: R −→ R is called a generalized derivation on R if there exists a derivation d: R−→Rcommutes with ∗ such that F(xy) = F(x)y +xd(y) holds for all x,y ∈ R. In the present paper, we shall show that L is contained in the center of R such that R admits a generalized derivations F and G with associated derivations d and g commute with ∗ satisfying several conditions.

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