Lie ideals and generalized (α, β )-derivations of *-prime rings Nadeem ur Rehman Email author Radwan Mohammed AL-Omary Shuliang Huang Article

First Online: 17 April 2012 Received: 21 October 2011 Accepted: 21 March 2012 DOI :
10.1007/s13370-012-0075-9

Cite this article as: Rehman, N.u., AL-Omary, R.M. & Huang, S. Afr. Mat. (2013) 24: 503. doi:10.1007/s13370-012-0075-9 Abstract Let (R , *) be a 2-torsion free *-prime ring with involution *, L ≠ 0 be a square closed *-Lie ideal of R and α, β automorphisms of R commuting with *. An additive mapping F : R → R is called a generalized (α, β )-derivation on R if there exists an (α, β )-derivation d such that F (xy ) = F (x )α (y ) + β (x )d (y ) holds for all \({x, y \in R}\) . In the present paper, we shall show that \({L\subseteq Z(R)}\) such that R is a *-prime ring admits a generalized (α, β )-derivation satisfying several conditions, but associated with an (α, β )-derivation commuting with *.

Keywords *-ideals *-prime rings Derivations and generalized (α, β )-derivations N. Rehman’s research is supported by UGC, India, Grant No. 36-8/2008(SR).

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© African Mathematical Union and Springer-Verlag 2012

Authors and Affiliations Nadeem ur Rehman Email author Radwan Mohammed AL-Omary Shuliang Huang 1. Department of Mathematics Aligarh Muslim University Aligarh India 2. Department of Mathematics, Al-Naderah Faculty Ibb University Ibb Yemen 3. Department of Mathematics Chuzhou University Chuzhou People’s Republic of China